The 30-year-old averaged 9.6 points, 7.6 rebounds and 2.4 assists in 20.2 minutes per contest with the Rockets this season.
Cousins signed with the Lakers prior to last season, but after he suffered a torn ACL during a pickup game that cost him the entire campaign, L.A. parted ways with him.
The four-time All-Star was one of the best players in basketball as recently as the 2017-18 season when he was with the New Orleans Pelicans, but a torn Achilles cut that year short after 48 games.
Cousins then appeared in just 30 regular-season games the following year with the Golden State Warriors after recovering from the Achilles tear. He suffered a torn quad in the playoffs that season, limiting him to eight playoff appearances.
During a five-season stretch from 2013-14 through 2017-18 with the Sacramento Kings and Pelicans, Cousins was named an All-Star four times and established himself as a premier NBA center with averages of 25.2 points, 11.9 rebounds, 3.9 assists, 1.5 steals and 1.4 blocks per game.
Cousins has come nowhere close to replicating those numbers since tearing his Achilles, but he is still a versatile big capable of contributing in limited minutes.
The problem for Cousins this season has been efficiency, as he is shooting just 37.6 percent from the field, the worst figure of his career by far.
Given his age and offensive struggles, it makes sense for the Rockets to move on from him. Houston is highly unlikely to make the playoffs at 11-18, and cutting ties with Cousins opens up more playing time for younger guys such as Jae'Sean Tate and Justin Patton.
As for the Lakers, they could use some frontcourt depth, especially with Anthony Davis currently on the shelf with Achilles and calf injuries.
The Lakers have struggled without Davis, as they are in the midst of a three-game losing streak and have fallen to 22-10 on the season, leaving them in a tie with the Los Angeles Clippers for second place in the Western Conference.
Cousins won't be a long-term answer, but he could be a quality fill-in until Davis returns before settling into a more fitting bench role.