The micro-blogging platform's shares soared nearly 18 per cent in pre-market trading after the news broke.
Musk is offering to "acquire all of the outstanding Common Stock of the Issuer not owned by the Reporting Person for all cash consideration valuing the Common Stock at $54.20 per share," read the filing.
Musk says Twitter needs to go private to go through the changes that need to be made.
"I would need to reconsider my position as shareholder," he added. "I invested in Twitter as I believe in its potential to be the platform for free speech around the globe, and I believe free speech is a societal imperative for a functioning democracy," Musk said in the fresh filing.
"However, since making my investment I now realise the company will neither thrive nor serve this societal imperative in its current form. Twitter needs to be transformed as a private company," he added.
Earlier this week, Twitter CEO Parag Agrawal announced that Musk will not join the board of the company, saying that "he believes it is for the best".
The Indian-origin CEO last week said the micro-blogging platform has appointed Musk to its board of directors. Musk, who acquired 9.2 per cent share in the micro-blogging platform for nearly $3 billion, is limited from buying more than 15 per cent of Twitter's stock.
In a fresh letter to Twitter's board, Musk said he believes Twitter "will neither thrive nor serve societal imperative in its current form".
"If the deal doesn't work, given that I don't have confidence in management nor do I believe I can drive the necessary change in the public market, I would need to reconsider my position as a shareholder," he added.
Musk has hired Morgan Stanley as his adviser for the takeover.
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