Billionaire entrepreneur Elon Musk is acquiring Twitter for $44 billion.
This was announced by the US short message service on Monday.
The purchase negotiations only started on Monday night.
Last week, Twitter's board of directors tried to prevent a takeover by the richest person in the world.
Twitter shareholders will therefore receive $54.20 per share - an offer that the Tesla boss had previously described as his "best and last".
Twitter shares rose 6 percent.
Musk has already announced that he intends to take the US company private.
Musk announced his intention to take over Twitter around ten days ago - and explained this with alleged restrictions on freedom of speech on the short message service, which he wanted to turn off.
The board of directors of the online service then introduced a countermeasure that allows other shareholders to buy shares at lower prices as soon as an attacker like Musk has a stake of more than 15 percent.
At the same time, Twitter generally reserved the right to agree to a deal.
Musk had already bought a good nine percent stake in the past few months.
Criticism of Musk's plans
The 50-year-old is one of the most active prominent Twitter users and has around 83 million followers.
He announced that he wants to make Twitter a "global platform for free speech" because it is important for civilisation.
Musk's promises of looser regulation drew criticism from pundits like former Facebook security chief Alex Stamos.
You don't increase the value of a platform by letting it be 99.9 percent filled with pornography and ads for fake branded sunglasses and sexual enhancers, he wrote on Twitter.
Musk's criticism of the state of free speech on Twitter is popular with supporters of former President Donald Trump and other US conservatives.
Among other things, they have long railed against the fact that Twitter and other online platforms are taking action against false information about the corona virus and Trump's uncovered allegations of election fraud.
Trump was banned from Twitter after expressing sympathy for his supporters who stormed the US Capitol in Washington on January 6, 2021.
The management has so far emphasized that there is no way back to the platform for the ex-president.
Musk's approaches could now make Trump sit up and take notice with a view to running again in the 2024 presidential election: he finds temporary "timeouts" better than permanent exclusions, said the Tesla boss in general.
In the early days, Musk downplayed the dangers of the virus himself and criticized restrictions in California as "fascist".
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