The world's richest man pays $ 54.2 per share.
Wednesday's closing price was $ 45.85.
Following the announcement, the Twitter price rose sharply in the negotiations.
Musk's bid for the remaining shares in Twitter is non-binding.
He calls it a "best and final" offer.
Reported after previous purchases
On April 4, the 50-year-old super-entrepreneur announced that he had bought up 9.1 percent of the shares in the microblog.
The result was a report to a court in New York with reference to investor rules on the reporting obligation when holdings reach five percent of the company.
Musk is said to have reached that level as early as March 14.
According to the Finance Act, he should have reported the information by 24 March.
According to the report, Musk is accused of having kept his purchases of shares on Twitter secret in order to keep the price down.
Tweeted about changes
On Thursday, his bid became known when documents were received by the US Financial Supervisory Authority SEC.
In the past week, the Tesla founder has tweeted extensively about things he wants to change on Twitter, such as making the service ad-free - despite the fact that close to 90 percent of the company's revenue last year came from ads.
Previously, his Twitter acquisition has been linked to a board position as the company's largest owner.
How the hostile action ends now remains to be seen.