Financial terms of the deal were not disclosed but multiple media reports said the Browns, which Forbes estimates at being worth $977 million, were sold for over $1 billion.
Lerner, who owns Premier League football club Aston Villa, was approached by Pilot Flying J Chief Executive Jimmy Haslam several weeks ago and said the proposal just made sense.
"While as a fiduciary I have always felt it was my responsibility to listen to offers, I had not been approached with a proposal that felt as natural and complete as Mr. Haslam's," Lerner, who took control of the Browns in 2002 after the death of his father, Al, said in a statement.
"He had done a lot of work on the Browns and the city of Cleveland and first and foremost gave me his personal assurance the team would remain in Cleveland."
The deal still has to be approved by NFL owners before it can be formally completed and that process is likely to be completed in October.
The Browns have failed to make the play-offs since losing in the wild-card round of the 2002 NFL season.
Haslam, who will need to divest the minority stake he holds in the Pittsburgh Steelers, expressed a desire to rejuvenate the Browns and connect with a Cleveland fan base that lost an NFL team to Baltimore in 1996 and were without a team until 1999.
"To own such a storied franchise as the Cleveland Browns, with its rich tradition and history, is a dream come true," the 58-year-old said. "We are committed to keeping the team in Cleveland and seeing it get back to the elite of the NFL - something all Browns fans want and deserve."
Lerner's departure will allow him to focus his energy and resources on improving the fortunes of Villa, who have also struggled in recent seasons.
He is expected to watch the Browns practice on Friday and then hold a news conference, according to local media reports.
"I feel a deep debt of gratitude to the loyal and passionate (Browns) fan base, as well as the people I've met and worked with over the years," said Lerner.
"It has been a privilege to be involved with the Cleveland Browns and my only hope is that the Haslam family has the best of luck and that the Browns are restored to their rightful place among NFL champions."