The letter was addressed to Bret Taylor, the chair of the Twitter board, not CEO Parag Agrawal, who assumed that title last fall. It concludes: "Twitter has extraordinary potential. I will unlock it."

Twitter issued a statement Thursday confirming that it had received the offer. The company said its board would carefully review the proposal "to determine the course of action that it believes is in the best interest of the company and all Twitter stockholders." Twitter declined to comment as to when its board would meet to discuss the offer.

But it will be difficult for Twitter to reject Musk's bid at the price he is offering, said Dan Ives, tech analyst with Wedbush Securities.

"Musk is putting the Twitter board's backs against the wall," Ives said. "The premium is at a level that will be hard to see other bids occurring."

But to get a return on a bid this high, Twitter would need to do more to bring in subscriber revenue and cut costs, Ives said. Musk's commitment to use the company to promote greater free speech doesn't do much, if anything, to increase its profitability, Ives said.

"Musk making this about free speech is the exact opposite of what every other corporate raider would do about monetizing the company's value," he added. "It's historic and bizarre at the same time."

Musk has 81.6 million Twitter followers, far more than any other other CEO, and is a much more prolific tweeter than the handful of celebrities who have even more followers than he does.

Musk a frequent critic of Twitter

Last week, Musk disclosed he had been buying shares of Twitter since late January, and that he had spent $2.6 billion to accumulate 73.1 million shares, which at the time represented a 9.1% stake, according to what the company had disclosed at that point about the number of shares that are held by investors.

In February, Twitter announced a plan to repurchase $2 billion worth of shares in an effort to raise its stock price. It has since repurchased 37 million shares, according to a disclosure filing on Thursday, reducing the number of shares outstanding by that amount.

That reduction in total shares increased Musk's stake to 9.6% without him having to purchase even one additional share. And it reduced the total value of the company by $2 billion based on Musk's $54.20 offer price.

After Musk's stock purchase disclosure, he initially accepted an offer of a seat on the board, an agreement that included a cap on his total investment in the company at 14.9%.

Agrawal sent a memo to employees Thursday announcing that there would be a company-wide meeting Thursday afternoon to "discuss today's news and what's next."

"It's important that we all come together today as #OneTeam," he said in the brief notice of the meeting."

Musk ha been unusually silent on his plans for Twitter in the days since he declined the spot on Twiter's board. He has yet to spell out the specifics of what changes he wants at the company.

"Right now there's more questions than answers as to his next step," said Ives.

How Musk could pay for his purchase

Although Musk is the richest person on Earth, most of his $274 billion net worth is tied up in his holdings in the publicly-traded stock of Tesla and privately-held SpaceX, and he has been reluctant to sell shares of Tesla beyond what he needed to in order to pay taxes.

It's very possible that Musk won't need to sell Tesla shares and instead could use them as collateral to borrow the money he needs to buy Twitter, Ives said. Musk's Tesla shares are worth about $177 billion, even with the modest decline in premarket trading Thursday.

"Banks will be lining up to be part of the consortium of lenders to the world's richest person," said Ives.

And even if he sold the number of Tesla shares he would need to buy all the outstanding shares of Twitter, Musk still would have a controlling stake in the company.

"I don't see Musk and Agarwal sharing any candle-lit dinners," said Ives

Musk prefers privately-held companies

Musk's tweet about taking Tesla private, in which he said he had "funding secured" for the offer when he did not, got him in trouble with the SEC. He eventually had to give up the position as chairman of Tesla, and agree to have his tweets with material information about Tesla reviewed by other executives at the company.

Taking a company private, or keeping it private, reduces the oversight the watchdog agency has on its operations.

The price he suggested for Tesla at that time, $420 a share, was seen highlighting April 20, the unofficial holiday of marijuana enthusiasts. This time, Musk's $54.20 per share offer for Twitter also includes "4.20."

— Donie O'Sullivan, Brian Fung and Brian Stelter contributed to this article.