Twitter Inc. and activist hedge fundElliott Management Corp. have agreed to a truce that will shake up the social-media company’s board but leave its Chief Executive Jack Dorsey in place.

The agreement calls for Twitter to appoint two new board members, with a promise to search for a new independent director, and make $2 billion in share repurchases, the company said. The buyback is to be funded in part by a $1 billion investment from technology-focused investment firm Silver Lake.

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