Morse, 26, joined the Kansas City Chiefs as a second-round draft pick (49th overall) from Missouri in 2015. He immediately became a starter and opened each of the 52 games, regular season and playoffs, he played in for Kansas City.
Morse started 15 games as a rookie but wasn't available for either of the Chiefs' two playoff games that year because of a concussion. He was limited to seven games in 2017 and 11 in 2018, plus two in the playoffs, because of injuries.
During last season, the Chiefs re-signed two interior offensive linemen, Cam Erving and Austin Reiter, in case they lost Morse in free agency. Reiter started four games during Morse's absence last season.
ESPN's Adam Teicher contributed to this report.