SAN FRANCISCO—Sam Altman’s bid to return to OpenAI after being ousted Friday faltered late Sunday, as the board that fired him refused to agree to the proposed terms of his reinstatement and quietly found someone else to take Altman’s spot.

Emmett Shear, former chief executive of Twitch, was named interim CEO, according to people with knowledge of the matter. Altman was shocked by the decision, previously feeling confident he would be able to return to the company he co-founded, according to a person familiar with his thinking.