Innate said on Monday that Mahjoubi would take over as chief executive on Dec. 30, replacing Herve Brailly who is moving on to become chairman of the supervisory board.
The loss of Mahjoubi is a setback for AstraZeneca, given the British drugmaker's focus on new cancer treatments. Mahjoubi previously worked at Roche's (ROG.S) Genentech unit before joining AstraZeneca, where he has helped lead oncology strategy.
His departure comes ahead of key clinical trial read-outs for the company's experimental immunotherapy drugs.
AstraZeneca said Mahjoubi's successor would be announced shortly.
For Mahjoubi, the move to Innate offers the opportunity to run a company that specialises in immuno-oncology, which is now transforming the fight against several different types of cancer.
Innate said he would be paid a base salary of 470,000 euros ($490,000). He will also get free shares in the company and be eligible for pay and share bonuses, if certain targets were met.
Shares in Innate were 4 percent higher by 1230 GMT while AstraZeneca slipped 1.4 percent.
Reporting by Ben Hirschler; Editing by Keith Weir