Ian Rapoport of NFL Network later reported the deal is worth $36 million. The signing cannot become official until the new league year begins Wednesday.
Richardson tallied 49 total tackles and 4.5 sacks in 2018 with the Minnesota Vikings, who signed him as a free agent after he spent the 2017 season with the Seattle Seahawks. Pro Football Focus graded him as the NFL's 47th-best interior defender.
Along with the solid production, the 28-year-old also transformed himself into a locker room asset after past issues, including a four-game suspension in 2015 while with the New York Jets for a violation of the league's substance-abuse policy.
"Life happens," Richardson told Chris Tomasson of the Pioneer Press in December. "I have a daughter now. I want to be a positive impact. I tell people now that I'm 'slow motion.' I ain't going nowhere too fast. I'm definitely on the straight and narrow now. I grab me a drink once in a blue moon, but that's about it."
The University of Missouri product racked up 44 total tackles, a sack, an interception and a forced fumble across 15 appearances for Seattle in 2017.
His track record across four years with the Jets, who selected him with the 13th overall pick in the 2013 draft, included the NFL Defensive Rookie of the Year Award in 2013 and a Pro Bowl selection in 2014.
The 6'3", 295-pounder also possesses positional versatility with the ability to play either defensive end or defensive tackle depending on the scheme.
Richardson will be playing for his third different team in as many years after signing with the Browns. While changing squads that often can have a negative impact, the tackle made a smooth transition to Minnesota, which lessens those concerns.
He should slot in as a starting defensive tackle on a Cleveland team that has strengthened its front four considerably this offseason with the signing of Richardson and the trade acquisition of Olivier Vernon from the New York Giants.