Mr Musk, who made the shock bid less than two weeks ago, said Twitter had “tremendous potential” that he would unlock. He also called for a series of changes from relaxing its content restrictions to eradicating fake accounts.
The firm initially rebuffed Mr Musk’s bid, but it will now ask shareholders to vote to approve the deal.
Mr Musk, the world’s richest person, promised to “make Twitter better than ever” and protect Twitter as the “digital town square where matters vital to the future of humanity are debated”.
Twitter’s board confirmed that Mr Musk’s $54.20-a-share bid had been unanimously accepted, 11 days after it was first announced. It comes little more than a week after Twitter had revealed a “poison pill” defence designed to prevent Mr Musk, 50, buying the social network.
The deal will take publicly-held Twitter private and make Mr Musk, who owns 9.1pc of the company, its 100pc owner. Twitter said the deal was expected to close this year, but would first need the approval of shareholders and regulators.
“Free speech is the bedrock of a functioning democracy, and Twitter is the digital town square where matters vital to the future of humanity are debated,” Mr Musk said.
“I also want to make Twitter better than ever by enhancing the product with new features, making the algorithms open source to increase trust, defeating the spam bots, and authenticating all humans. Twitter has tremendous potential – I look forward to working with the company and the community of users to unlock it.”
It is not clear who will lead the new company. The firm is currently led by Parag Agrawal, who took over from co-founder and former boss Jack Dorsey last November.
But in his offer document, Mr Musk told Twitter’s board: “I don’t have confidence in management.”
Mr Musk is the world’s richest man, according to Forbes magazine, with an estimated net worth of $273.6bn mostly due to his shareholding in electric vehicle maker Tesla which he runs. He also leads the aerospace firm SpaceX.