The 21-year-old French defender has already agreed on personal terms in a five-year deal with the option for an extra year.
Fofana has been a long-term target for the Blues this summer having missed out on other defensive targets.
Leicester boss Rodgers had recently stated his desire to keep the center-back at the club this summer, with the Foxes rejecting three significant bids for the Frenchman.
According to reports, the fee Chelsea would pay could exceed the one paid by Manchester United to sign Harry Maguire in 2019, with Fofana's deal believed to be around £70m plus add-ons as per Sky Sports.
Leicester are also understood to have been lining up a replacement for the last few days to allow the deal to go through.
Fofana was already ruled out of the Foxes' clash with Chelsea on Saturday after Brendan Rodgers deemed him not in the right frame of mind to play.
However, on the eve of the Premier League match, the Blues have finally reached a breakthrough for the defender.
Chelsea Transfer News
Chelsea will likely also push for more signings as their summer spending reaches a staggering £245m with the imminent arrival of Fofana.
Chelsea are currently holding talks for Dinamo Moscow midfielder Arsen Zakharyan, who has a £12.6m release clause.
While talks with Barcelona for Pierre Emerick-Aubameyang also continue as well as the Blues remain hopeful of signing a striker this summer.
The Londoners still remain interested in Everton winger Anthony Gordon after two bids worth up to £45m were rejected by the Merseyside club.