Musk has already floated ideas for changes he wants to make at Twitter.
The sale is for $54.20 a share, or around $44 billion in total.
Negotiations between the two parties stretched into the early hours of Monday morning.
Twitter’s board initially met Sunday morning to discuss the potential sale.
The entrepreneur, who already runs Tesla, SpaceX and other companies.
Tesla founder and a notorious Twitter troll, acquired 9.2 percent of Twitter earlier this month, making him the company’s largest shareholder.
Twitter set a goal to reach $7.5 billion in revenue and 315 million users by 2023.
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