Mr Lebedev has already bought the Evening Standard in the UK
Alexander Lebedev moved closer to control of the Independent newspapers after the deal was allowed by the Office of Fair Trading (OFT).
The UK regulator said it will not investigate the deal between Mr Lebedev and Independent News & Media (INM) over competition issues.
"There is no competition barrier," said a spokesperson for the OFT.
The Russian billionaire already owns 75% of another UK paper - the London Evening Standard.
Lebedev and INM entered an exclusive non-binding agreement about the Independent and its sister paper, the Independent on Sunday in December.
But talks have dragged on and it is understood that there have been in discussions over issues including INM's £35m printing contract and a deal surrounding office space in Kensington.
Shareholders, who were previously bond holders, will be keen for a deal.
Part of the agreement they made with INM after agreeing to repay 200m euros (£179m) debt last year, is for the sale of the loss-making papers as soon as is practically possible.
INM is expected to report financial results on Wednesday next week.