The proposal has now been sent to the government and Premier League for approval.
With just over three weeks remaining on the club's current operating licence, which expires on 31 May, Boehly is on course to complete his takeover by the end of this month.
Russian owner Roman Abramovich, now subject to sanctions by the British government, put the London club up for sale in early March following his country's invasion of Ukraine.
Abramovich cleared the path for the takeover on Thursday after he dismissed reports that he wanted a loan given to the club, reportedly worth £1.5 billion, to be repaid.
The Boehly group, which also includes Swiss billionaire Hansjorg Wyss and British property investor Jonathan Goldstein, were in exclusive negotiations to buy the club after a late bid from British billionaire Jim Ratcliffe was rejected.
Groups led by Boston Celtics co-owner Stephen Pagliuca and former British Airways chairman Martin Broughton were earlier eliminated from the bidding process while a consortium led by Chicago Cubs owners the Ricketts family pulled out of the running.