For a decade, Eric Schmidt ran Google as chief executive and as the “adult” in the room, mentoring the internet company’s young founders, Larry Page and Sergey Brin. In 2011, Mr. Schmidt handed control of Google back to Mr. Page. He has not taken another C.E.O. job since.

But on Monday, Mr. Schmidt told employees of Relativity Space, a rocket start-up in Long Beach, Calif., that he had made a significant investment and taken a controlling stake in the company, and would take over as chief executive, two people with knowledge of the meeting said.

Mr. Schmidt, 69, succeeds Relativity Space’s current chief and co-founder, Timothy Ellis, the two people said. It is unclear how much money Mr. Schmidt has invested in the start-up.

Relativity Space is one of a crop of start-ups angling to manufacture rockets that can carry smaller payloads of around two tons or less, up to low to medium Earth orbit. Some of these companies focus on building cheaper, reusable rockets to launch commercial payloads — usually satellites — into space for a fraction of the cost of legacy manufacturers that use pricier, disposable rockets.

Elon Musk, left, the chief executive of SpaceX, spoke with Eric Schmidt last month. Relativity Space is aiming to compete with SpaceX in launching satellites to space. Al Drago for The New York Times

The aim would partly be to take on Elon Musk’s SpaceX, the dominant rocket maker. Relativity Space has also said it has a long-term goal of creating an industrial base on Mars.

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