It's set to be the second biggest kit deal in the Premiership after Adidas' deal with Manchester United, worth £75 million ($108 million) a season.
The news comes as Chelsea ended its deal with Adidas six years early last week.
It cost the team £40 million to get out of the agreement, with Adidas imposing restrictions on when Chelsea could announce a new deal, according to Bloomberg.
Chelsea is one of the richest in the world, coming eighth in Deloitte's Football Money League report. It made £332 million in the 2015/16 season.
The club was bought by Russian billionaire Roman Abramovic back in 2003, and his investment in the team saw it win four Premier League titles - most recently in the 2014/15 season.
But Chelsea struggled last season, firing manager Jose Mourinho after a poor start. It eventually finishing tenth in the league, which was won by Leicester City.
Chelsea's director Marina Granovskaia is believed to have struck the new Nike deal, the Telegraph says, which adds to its existing £40 million a year deal with Yokohama tyres and a £10 million training kit deal with Carabao. While the timespan of the Nike deal is unconfirmed, most big kit agreements last for at least 10 years.
The club could not be immediately reached for comment on the deal.