All that remains is for the Office of Fair Trading to give the sale the go-ahead, which would see the deal complete before the end of April.
Lebedev and INM had been in talks over the titles but Lebedev had said he was only prepared to back five years of an existing print contract with Trinity Mirror.
According to reports, it would have cost INM £32m to get out of the 10-year contract with Trinity Mirror, which it has now agreed to guarantee half of.
It is understood that Lebedev, who bought London's Evening Standard last year, has paid £1 for the titles, but he has promised to pump millions of pounds into them.
The media is already speculating that he will drop the cover price of the title to below £1 to put pressure on its main rival The Guardian. It is also rumoured that he could follow the system he used with The Evening Standard and take the title free to boost circulation and advertising revenues.