Musk's plan to take Tesla private would give all shareholders the option to stay as investors in the now-private company or to sell their shares at $420 per share, which represents a premium of about 20 percent based on the stock price during the second quarter earnings call at the end of June.
Any final decision about privatizing the company would fall to existing shareholders.
Musk mused Tesla could be bought back at $420 per share.
If the content of Musk's tweet was not true, lawyers argue, it could expose Tesla's mercurial chief executive officer and the company to regulatory action and private lawsuits.
The statement by the board, published by NASDAQ, confirms that the proposal is under serious consideration.
On Tuesday morning, Musk emailed a statement to Tesla employees.More news: Liverpool wrap up impressive pre-season with win against Torino
"Distraction or not, the move feels right even if Musk is downplaying how supportive public markets have been".
Cowen analyst Jeffrey Osborne told clients in a note Wednesday that he didn't believe Tesla's current business "support a valuation anywhere close to $420 per share".
Tesla shares fell as much as 3.4 per cent to US$366.52 before the start of regular trading, though they pared declines after the board statement. But going private could also complicate Tesla's effort to build a mainstream electric vehicle by removing the easy access to capital the Wall Street darling has enjoyed.
They said this "included discussion as to how being private could better serve Tesla's long-term interests". But I didn't walk away from it thinking, .
"Only reason why this is not certain is that it's contingent on a shareholder vote", Musk said in one tweet. He followed up the tweet with an email to Tesla employees saying that he thought "the best path forward" would be to take Tesla private. "Either way, the future is very bright, and we'll keep fighting to achieve our mission".
But the board offered no further details of the proposal or its funding, sparking new questions about the feasibility of the master gambit Musk revealed in a surprise series of midday tweets on Tuesday.
The oil-rich kingdom of Saudi Arabia's investment fund has gobbled up a multibillion-dollar stake in the company in recent months, the Financial Times reported Tuesday, but Tesla has not answered questions about the involvement of the kingdom, or anyone else, in how he would finance the company's exit from public markets.
Days after Tesla opened up the Model 3 configurator to all potential buyers, not just reservation holders who got a place in line over a year ago, uncomfortable math lingers over the automaker's.