On Monday, the Premier League said the consortium had passed its owners' and directors' test. The deal still needs to be approved by the European Commission because Abramovich has a Portuguese passport.
But there is now optimism in the Boehly-led consortium that the process to buy Chelsea should be wrapped up before the May 31 deadline set by the Government.
A Government spokesperson said: “Late last night the UK Government reached a position where we could issue a licence that permits the sale of Chelsea Football Club.
“Following the sanctioning of Roman Abramovich, the Government has worked hard to ensure Chelsea Football Club has been able to continue to play football. But we have always been clear that the long-term future of the club could only be secured under a new owner.
“Following extensive work, we are now satisfied that the full proceeds of the sale will not benefit Roman Abramovich or any other sanctioned individual. We will now begin the process of ensuring the proceeds of the sale are used for humanitarian causes in Ukraine, supporting victims of the war.
“The steps today will secure the future of this important cultural asset and protect fans and the wider football community. We have been in discussions with relevant international partners for necessary licences required and we thank them for all their cooperation.”
Ministers have been locked in talks for weeks over how to handle the proceeds and the £1.6bn in loans Abramovich made to Chelsea, which he has always insisted he would write off.
Now common ground has been reached on that issue, ministers are said to be in “intense discussions” with counterparts at the European Union and in Portugal to provide them the assurances they need to push the deal over the line.
Timing is tight and ministers fear Chelsea’s future will be at risk if deadlines for the club participating in the Premier League and Champions League next season are not met.
A deadline set by UEFA for Chelsea to register for next season’s Champions League is not until next Tuesday, but it is understood the process of moving the money involved in the deal needs to start imminently to ensure it is completed by the time of that deadline.
The Premier League meet next Thursday to hand out licenses for next season.