The Lakers signed Morris via the $1.75 million disabled player exception they received for Cousins earlier this season, league sources told ESPN's Adrian Wojnarowski.
Morris negotiated a buyout with the Detroit Pistons on Friday, leaving $4.3 million (the remainder of this season and his 2020-21 salary) on the table, according to reporting by ESPN's Bobby Marks.
Morris, 31, appeared in 44 games for the Pistons this season, averaging 11 points and 3.9 rebounds per game. He's able to play both forward spots and is a good rebounder and defender. Over nine seasons, he has averaged 11.6 points, 5.4 rebounds and 1.7 assists in 623 games.
The LA Clippers' Marcus Morris, Markieff's twin brother, said Saturday that he can see himself living with Markieff and carpooling to Staples Center if the Clippers and Lakers were to face each other in a seven-game playoff series.
Cousins, a popular player in the Lakers' locker room, has not played this season because of a torn ACL in his left knee. The league granted the Lakers a disabled player exception for Cousins because the injury was expected to keep him out the entire season.
A four-time All-Star, Cousins has roughly $1 million left on his $3.5 million contract. A team claiming him off of waivers would have non-Bird rights and could offer him a contract worth up to $4.2 million (or midlevel exception/cap space) as a free agent.