House's agent Mark Bartelstein said Thursday that the second year is a player option.
House was a second-round draft pick by the Heat in 2000 and spent his first three NBA seasons with them. He has since played for eight other teams, including Boston and New York last season, when he averaged 7.0 points in 68 games off the bench.
The Celtics and Bulls were among several teams that showed interest in House this offseason.
His career average is 7.6 points, and he's a 39 percent shooter from 3-point range, with a reputation for making clutch baskets.
Information from The Associated Press was used in this report.