The Rockets were limited to offering the veteran's minimum to Cousins, who missed all of last season with a torn ACL in his left knee suffered after he signed with the Los Angeles Lakers.
"Grateful for the opportunity and excited for what's ahead," he told Spears.
However, Cousins' career has been interrupted by a series of serious injuries over the past three years.
Cousins ruptured an Achilles tendon in February 2018 while playing for the Pelicans in a win over the Rockets. That injury caused his value in free agency to plummet, and Cousins signed with the Golden State Warriors for $5.3 million that summer.
Cousins missed much of his season with the Warriors while in rehab for his Achilles injury and was sidelined for much of Golden State's playoff run with a torn quadriceps. He averaged 16.3 points, 8.2 rebounds and 3.6 assists in 30 games with the Warriors.
After committing to full-time small ball in the middle of last season, starting 6-foot-5 P.J. Tucker at center, the Rockets have agreed to deals this offseason with a pair of centers who have been prolific scorers.
Houston agreed with former Detroit Pistons center Christian Wood on a three-year, $41 million contract in the opening hours of free agency Friday, sources said. Wood, 25, averaged 13.1 points per game last season, including 21.9 points during a 12-game stint as a starter after Detroit traded Andre Drummond.
They should help play a role in aiding the Rockets' rebounding woes. Since Jan. 31, Houston had a 44.6 rebounding percentage, which was last in the NBA over that span and would have ranked last by any team in a full season since 1996-97.