Elon Musk has offered to buy Twitter for about $41 billion, just days after rejecting a seat on the social media company’s board.

Musk’s offer price of $54.20 per share was disclosed in a regulatory filing. Twitter’s shares jumped 12 per cent in pre-market trading.

The offer represents a 38 per cent premium to Twitter’s closing price on April 1, the last trading day before it was revealed that the billionaire had become the micro-blogging site’s biggest shareholder with a stake of more than 9 per cent.

Musk said in a letter to the Twitter chairman Bret Taylor: “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.

“My offer is my best and final offer and if it is not accepted, I would need to reconsider my position as a shareholder,” he said.

Earlier this week, he abandoned a plan to join Twitter’s board, just as his tenure was about to start. Taking the board seat would have prevented him from a possible takeover of the company.

Last night Twitter shares closed up 3.1 per cent, or $1.37, at $45.85, valuing the company at nearly $37 billion.

Twitter, based in San Francisco, owns one of the world’s largest social networks. It was set up in 2006 and makes most of its money through advertising. The group went public in November 2013.

Musk leads Tesla, the electric carmaker, and SpaceX, the space exploration business. He is the world’s richest man with a personal fortune of $273 billion, according to Forbes, following the extraordinary rally of shares in Tesla, which is now worth more than $1 trillion.

In recent months he has used his account on the platform to both criticise the service to his 81 million-plus followers and propose a series of changes. Last weekend he asked whether Twitter was “dying” due to many of its most-followed accounts, including those belonging to Justin Bieber and Taylor Swift, not tweeting frequently.

Musk also proposed a shake-up of Twitter’s premium subscription service. He suggested that there should be no ads on Twitter Blue because the “power of corporations to dictate policy is greatly enhanced if Twitter depends on advertising money to survive”.

Parag Agrawal, Twitter’s chief executive, had warned staff of “distractions ahead” after Musk rejected his invitation to join the company’s board. The company has yet to comment on the offer.