Finney-Smith had missed the first couple of months of the season as he recovered from ankle surgery in the summer, and will subsequently be on a strict minutes restriction in his first game back.
The 32-year-old spent the 2024-25 season split between the Brooklyn Nets and Lakers after being dealt to L.A. midway through the year.
In 63 games split between the two squads, Finney-Smith averaged 8.7 points, 3.9 rebounds, 1.4 assists and 0.9 steals while shooting 41.1 per cent from beyond the arc.
The 3-and-D specialist opted to join Houston via free agency in the off-season, agreeing to a four-year, $52.7-million deal.
He’ll now join a Rockets team that sits sixth in the Western Conference — 1.5 games behind the Lakers — with a 17-10 record.