He says it needs to be transformed as a private company in order to build trust with users and do better at serving what he calls the “societal imperative” of free speech.
Twitter said it will become a privately held company after the sale is closed.
“Twitter has a purpose and relevance that impacts the entire world,” CEO Parag Agrawal said in a tweet.
“Deeply proud of our teams and inspired by the work that has never been more important.”
Mr Musk describes himself as a “free-speech absolutist,” although he has not been exactly clear what he means by that.
In a recent TED interview, the billionaire said he would like to see Twitter err on the side of allowing speech instead of moderating it.
He said he would be “very reluctant” to delete tweets and would generally be cautious about permanent bans. He also acknowledged that Twitter would have to abide by national laws governing speech in markets around the world.
Mr Musk himself, though, regularly blocks social media users who have criticised him or his company and has used the platform to bully reporters who have written critical articles about him or his company.
Twitter’s board at first enacted an anti-takeover measure known as a poison pill that could have made a takeover attempt prohibitively expensive.
But when Mr Musk outlined the financial commitments he had lined up to back his offer of 46.5 billion dollars — and no other bidders emerged — the board opened negotiations with him.