https://www.bbc.com/news/business-63137114
In a letter to the firm, Mr Musk agreed to pay the price he offered months ago before trying to quit the deal.
The surprise reversal comes just weeks before the two sides were due in court.
Twitter, which had sued Mr Musk to force the takeover to move forward, was seen as having the stronger case.
In the letter, attorneys for Mr Musk said he intended to move ahead to complete the transaction, pending receipt of the financing and an end of the legal fight.
A spokesperson for Twitter acknowledged the firm had received the proposal, adding "the intention of the company is to close the transaction at $54.20 per share" - the price that Mr Musk promised in April.