Smith was released by the Detroit Pistons on Monday having signed a four-year deal worth $54 million in July 2013.
The 29-year-old forward - pick 17 in the 2004 NBA draft - is now to set to be reunited with former college team-mate Dwight Howard in Houston, despite reported interest from the Dallas Mavericks, Miami Heat, Sacramento Kings, Los Angeles Clippers and Memphis Grizzlies.
"It's an exciting time for me," Smith said in an interview with FOX26 Sports.
"Being able to be reunited with a good friend and one of the best teammates I ever played with, I think we can definitely do something special.
"Playing beside the best two-guard [shooting guard] in the game right now in James Harden, what more can you ask for."
Smith added: "I think I can add to their toughness.
"I think I can add to their versatility at the four position, being able to pass the basketball and score the ball down low.
"Just add another basketball IQ, which will help when we make it to the post-season."
The Rockets are fourth in the Western Conference with a 20-7 win-loss record.