House is remaining in Houston on a three-year deal worth $11.1 million, according to sources. Green will be back with the Rockets on a one-year deal, his agent James Dunleavy told ESPN.
The new contract means Green's second stint with the Rockets is now the longest uninterrupted amount of time he's spent with any one franchise in his career. The Houston native enters the 13th season of his NBA career having played for eight different teams.
Green, 33, averaged 9.2 points per game and shot 35.4% from 3-point range in a reserve role for the Rockets last season.
Like Green, House is from Houston and has played for multiple teams in his career. When he joined the Rockets last year, it was his third stop in three seasons.
The 26-year-old House averaged 9.4 points, 3.6 rebounds and 1.0 assists per game last season.
NBA free-agent contracts can't be officially signed until Saturday.