The Chiefs sent over safety Eric Murray in the deal. Sources told the NFL Network that Ogbah, along with running back Duke Johnson, didn't report Monday for the start of the Browns' voluntary off-season workout program while the franchise explored trading the players.
The Browns originally drafted Ogbah in the second round of the 2016 NFL Draft. In three seasons with Cleveland, he started 40 games and recorded 122 tackles, 12.5 sacks and 29 quarterback hits.
Kansas City previously signed defensive end Alex Okafor in free agency. The additions of Ogbah and Okafor come after the Chiefs parted ways with pass rushers Justin Houston and Dee Ford this off-season. Houston signed a deal with the Indianapolis Colts and Ford was traded to the San Francisco 49ers.
Murray reunites with Browns general manager John Dorsey in Cleveland. Murray entered the league as a fourth-round pick in the 2016 draft while Dorsey served as the Chiefs' general manager.
The 25-year-old Murray replaces defensive back Derrick Kindred, who was released earlier Monday.
In three seasons in the league, Murray has played in 45 games (11 starts) and tallied 94 total tackles, one sack, one interception and seven passes defensed. He had 54 tackles, two passes defensed and one pick in nine starts last season.