Billionaire Elon Musk has reached an agreement to acquire Twitter for approximately US$44 billion ($66.4b), the company said.

The outspoken Tesla CEO, the world's wealthiest person, has said he wants to buy Twitter because he thinks it's not living up to its potential as a platform for "free speech." 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," its CEO Parag Agrawal said in a tweet. "Deeply proud of our teams and inspired by the work that has never been more important."

Musk describes himself as a "free-speech absolutist," although he hasn't been exactly clear what he means by that. In a recent TED interview, the billionaire said he'd like to see Twitter err on the side of allowing speech instead of moderating it.

He said he'd 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.

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 Musk outlined the financial commitments he'd lined up to back his offer of US$46.5b — and no other bidders emerged — the board opened negotiations with him.

Musk is the world's wealthiest person, according to Forbes, with a nearly US$279 billion fortune. But much of his money is tied up in Tesla stock — he owns about 17 per cent of the electric car company, according to FactSet, which is valued at more than US$1 trillion — and SpaceX, his privately held space company. It's unclear how much cash Musk has.

Musk began making his fortune in 1999 when he sold Zip2, an online mapping and business directory, to Compaq for US$307 million. He used his share to create what would become PayPal, an internet service that bypassed banks and allowed consumers to pay businesses directly. It was sold to eBay for US$1.5 billion in 2002.

That same year, Musk founded Space Exploration Technologies, or SpaceX, after finding that cost constraints were limiting Nasa's interplanetary travel. The company eventually developed cost-effective reusable rockets.

In 2004, Musk was courted to invest in Tesla, then a startup trying to build an electric car. Eventually he became CEO and led the company to astronomical success as the world's most valuable automaker and largest seller of electric vehicles.

- Tom Krisher and Matt O'Brien, AP