Exhibit 99.1

Radiopharm Theranostics Announces Concurrent
US$4.1 Million Registered Direct Offering and
Up To Additional A$12.7 (US$8.9) Million Australian Placement and Share Purchase Plan
New York, USA and Sydney, Australia, July 24, 2026 — Radiopharm
Theranostics Limited (ASX: RAD, Nasdaq: RADX, “Radiopharm” or the “Company”), a clinical-stage biopharmaceutical
company focused on developing innovative oncology radiopharmaceuticals for areas of high unmet medical need, today
announces that it has entered into a Securities Purchase Agreement (“SPA”) with certain U.S. accredited institutional investors
to issue, in a registered direct offering, 1,281,646 American Depositary Shares (“ADSs”), representing 384,493,800
ordinary shares (with each ADS representing 300 ordinary shares) of the Company, at an offering
price of US$3.16 per ADS, to raise aggregate gross proceeds of approximately US$4.1 million, before
deducting the placement agent fees and other offering expenses payable by the Company.
In a concurrent private placement
and pursuant to the terms of the SPA, the Company has agreed to issue to the investors unregistered warrants to purchase up to 1,281,646
ADSs. The warrants will be exercisable on or after the effective date of shareholder approval of
the issuance of the ordinary shares represented by ADSs issuable upon exercise of the warrants, will have an exercise price of US$3.79
per ADS and will expire on July 31, 2029.
The offering is expected to close on or about July 28, 2026, New York
Time, subject to the satisfaction of customary closing conditions.
H.C. Wainwright & Co. is acting as the
exclusive U.S. placement agent for the offering.
The ADSs offered in the registered direct
offering (but not the warrants issued in the private placement or the ADSs underlying such warrants) are being offered by the Company
pursuant to a “shelf” registration statement on Form F-3 (File No. 333-292178) that was filed with the Securities and Exchange
Commission (“SEC”) on December 16, 2025, and became effective on December 23, 2025. The registered direct offering of the
ADSs representing ordinary shares is being made only by means of a prospectus, including a prospectus supplement, forming a part of the
effective registration statement. A final prospectus supplement and the accompanying prospectus relating to and describing the terms of
the registered direct offering will be filed with the SEC. Electronic copies of the final prospectus supplement and the accompanying prospectus
relating to the registered direct offering may be obtained, when available, at the SEC’s website at www.sec.gov or by contacting
H.C. Wainwright & Co., LLC at 430 Park Avenue, 3rd Floor, New York, NY 10022, by telephone at (212) 856-5711 or by email at placements@hcwco.com.
The warrants described above are being issued in a concurrent private
placement under Section 4(a)(2) of the U.S. Securities Act of 1933, as amended (the “Securities Act”), and Regulation D promulgated
thereunder and, along with the ADSs representing ordinary shares underlying the warrants, have not been registered under the Securities
Act, or applicable U.S. state securities laws. Accordingly, the warrants and underlying ADSs representing ordinary shares may not be offered
or sold in the United States except pursuant to an effective registration statement or an applicable exemption from the registration requirements
of the Securities Act and such applicable state securities laws.
Radiopharm Theranostics Limited
Suite 1, Level 3, 62 Lygon Street,
Carlton South VIC 3053 Australia
ABN: 57 647 877 889

In addition to the registered
direct offering of ADSs and private placement of warrants in the United States, the Company has received firm commitments from
Australian institutional and professional investors in a private placement for approximately A$6.7 million (US$4.7 million), before
deducting the placement agent fees and other offering expenses payable by the Company, (“Australian Placement”). Due
to limitations on the Company’s capacity to issue new securities under the listing rules of the Australian Securities Exchange,
the issuance under the Australian Placement of 40.0 million ordinary shares, representing gross proceeds of A$0.6 million (US$0.4 million),
will be subject to shareholder approval.
The Company will also make a Share Purchase Plan available to shareholders
with registered addresses in Australia and New Zealand to raise up to an additional A$6 million (US$4.2 million), before
deducting the placement agent fees and other offering expenses payable by the Company. The Share Purchase Plan is subject to shareholder
approval.
Under the Australian Placement and the Share Purchase Plan, subscribers
and eligible shareholders are anticipated to receive one option for every one new ordinary share subscribed for. The options will have
an exercise price of A$0.018 per option, expiring on July 31, 2029, and will be subject to shareholder approval. The Company will apply
to ASX for official quotation of the options. If quotation is not approved, the options will be issued without quotation (as unlisted
options).
The Company expects to seek all approvals from shareholders at an extraordinary
general meeting to be held on or about Friday, September 11, 2026.
The Company currently intends to use the funds raised from the offers
of securities described above to support the commencement of the RAD101 registrational study, the progression of multiple therapeutic
programs through key clinical milestones, ongoing strategic partnering initiatives, and working capital and other general corporate purposes.
This
press release does not constitute an offer to sell, or the solicitation of an offer to buy, the securities described herein, nor will
there be any sale of these securities in any state or other jurisdiction in which such offer, solicitation or sale is not permitted. Any
securities to be issued under the Australian Placement and Share Purchase Plan have not been, and will not be, registered under the Securities
Act and may not be offered or sold in the United States except in transactions exempt from, or not subject to, the registration requirements
of the Securities Act and applicable U.S. state securities laws. Shareholders in the United States may not participate in the Share Purchase
Plan.
All references to “A$” are to Australian dollars and all
references to “US$” are to U.S. dollars.
Radiopharm Theranostics Limited
Suite 1, Level 3, 62 Lygon Street,
Carlton South VIC 3053 Australia
ABN: 57 647 877 889

For more information:
Riccardo Canevari
CEO & Managing Director
P: +1 862 309 0293
E: rc@radiopharmtheranostics.com
Anne Marie Fields
Precision AQ (Formerly Stern IR)
E: annemarie.fields@precisionaq.com
Media
Matt Wright
NWR Communications
P: +61 451 896 420
E: matt@nwrcommunications.com.au
About Radiopharm Theranostics
Radiopharm Theranostics is a clinical-stage radiotherapeutics company
developing a world-class platform of innovative radiopharmaceutical products for diagnostic and therapeutic applications in areas of high
unmet medical need. Radiopharm is listed on the ASX (RAD) and Nasdaq (RADX). The company has a pipeline of distinct and highly differentiated
platform technologies spanning peptides, small molecules and monoclonal antibodies for use in cancer. The clinical program includes one
Phase 2 and five Phase 1 trials in a variety of solid tumor cancers, including lung, breast, and brain metastases. Learn more at radiopharmtheranostics.com
Safe Harbor Statement:
This press release contains “forward-looking
statements” within the meaning of Section 27A of the U.S. Securities Act of 1933 and Section 21E of the U.S. Securities Exchange
Act of 1934, including, without limitation, statements by the Company relating to the completion of the offering, the Australian Placement
and the Share Purchase Plan, the satisfaction of customary closing conditions related to the offering, the receipt of shareholder approval
and the intended use of proceeds from the offering. Any forward-looking statements that may be in this press release are subject to risks
and uncertainties relating to market and other conditions, the difficulties in Radiopharm’s plans to develop and commercialize its
product candidates, the timing of the initiation and completion of preclinical and clinical trials, the timing of patient enrollment and
dosing in clinical trials, the timing of expected regulatory filings, the intellectual property position and the ability to procure additional
sources of financing. Accordingly, you should not rely on those forward-looking statements as a prediction of actual future results.
Radiopharm Theranostics Limited
Suite 1, Level 3, 62 Lygon Street,
Carlton South VIC 3053 Australia
ABN: 57 647 877 889