Appendix 3Y Change of Director’s Interest Notice + See chapter 19 for defined terms. 01/01/2011 Appendix 3Y Page 1 Rule 3.19A.2 Appendix 3Y Change of Director’s Interest Notice Information or documents not available now must be given to ASX as soon as available. Information and documents given to ASX become ASX’s property and may be made public. Introduced 30/09/01 Amended 01/01/11 Name of entity Mesoblast Limited ABN 68 109 431 870 We (the entity) give ASX the following information under listing rule 3.19A.2 and as agent for the director for the purposes of section 205G of the Corporations Act. Name of Director Dr Eric Rose Date of last notice 3 May 2024 Part 1 - Change of director’s relevant interests in securities In the case of a trust, this includes interests in the trust made available by the responsible entity of the trust Note: In the case of a company, interests which come within paragraph (i) of the definition of “notifiable interest of a director” should be disclosed in this part. Direct or indirect interest Indirect interest Nature of indirect interest (including registered holder) Note: Provide details of the circumstances giving rise to the relevant interest. Interest in ordinary shares held in the form of American Depositary Shares (“ADSs”) held by custodian JP Morgan Nominees Australia Pty Limited. Direct interest in the ADSs. Date of change 8 May 2024 No. of securities held prior to change 21,428 ADS 4,330,765 options *Please note, Dr Rose will be issued 5,039,814 ordinary shares subject to shareholder approval at the 2024 Annual General Meeting. Class American Depositary Shares. Each ADS represents 10 ordinary shares. Number acquired 19,734 ADS Number disposed Not applicable Exhibit 99.1

Appendix 3Y Change of Director’s Interest Notice + See chapter 19 for defined terms. Appendix 3Y Page 2 01/01/2011 Value/Consideration Note: If consideration is non-cash, provide details and estimated valuation US$151,207.83 (US$7.6623 per ADS) No. of securities held after change 41,162 ADS 4,330,765 options *Please note, Dr Rose will be issued 5,039,814 ordinary shares subject to shareholder approval at the 2024 Annual General Meeting. Nature of change Example: on-market trade, off-market trade, exercise of options, issue of securities under dividend reinvestment plan, participation in buy-back On-market share purchase on the Nasdaq Part 2 – Change of director’s interests in contracts Note: In the case of a company, interests which come within paragraph (ii) of the definition of “notifiable interest of a director” should be disclosed in this part. Detail of contract Not applicable Nature of interest Not applicable Name of registered holder (if issued securities) Not applicable Date of change Not applicable No. and class of securities to which interest related prior to change Note: Details are only required for a contract in relation to which the interest has changed Not applicable Interest acquired Not applicable Interest disposed Not applicable Value/Consideration Note: If consideration is non-cash, provide details and an estimated valuation Not applicable Interest after change Not applicable Part 3 – +Closed period Were the interests in the securities or contracts detailed above traded during a +closed period where prior written clearance was required? No

Appendix 3Y Change of Director’s Interest Notice + See chapter 19 for defined terms. 01/01/2011 Appendix 3Y Page 3 If so, was prior written clearance provided to allow the trade to proceed during this period? Not applicable If prior written clearance was provided, on what date was this provided? Not applicable