Although the agreement isn't the final step, the announcement means the Tesla founder is in the end game of acquiring the social media platform.
Twitter has reached an agreement for the billionaire Elon Musk to buy the social media platform in a $44bn (£34.6bn) deal.
The announcement follows, what were reported to be, extensive discussions between Musk and Twitter's board starting on Sunday that stretched into Monday.
Musk announced an offer to buy the social media platform on 14 April for $54.20 a share, or about $43bn.
The additional $1bn price tag is understood to reflect the purchase of additional shares revealed by Twitter.
The deal means Twitter is now on course to be taken private, ending its run on the stock market which began in 2013.
Its shares, briefly suspended for the announcement, were 6% up on the news but trading at $51 per share - well below the offer price or $54.20 - indicating that some scepticism remained over the takeover.