Cousins, 30, had worked out for the Rockets Monday.
Cousins averaged 16.3 points, 8.2 rebounds and 3.6 assists per game in 30 appearances with the Golden State Warriors during the 2018-19 season. The four-time All-Star missed all of last season with a torn ACL in his left knee as a member of the NBA champion Los Angeles Lakers.
Cousins was the No. 5 overall pick from Kentucky in the 2010 NBA Draft. He began his career with the Sacramento Kings and spent several years there until he was traded to the New Orleans Pelicans in 2017.
Cousins' career has been interrupted by numerous injuries, including a ruptured Achilles tendon in 2018 and a torn quadriceps, prior to his ACL tear.
The 2020-21 NBA season is scheduled to begin on Dec. 22 and each team will play 72 games, instead of the usual 82. Preseason training camp is planned to start Dec. 1. It's a much later start for the NBA due to the COVID-19-interrupted 2019-20 season, which pushed the playoffs from April to August. The Lakers beat the Miami Heat for the NBA title a little more than a month ago.