The deal was confirmed to the Associated Press by a person familiar with the negotiations who asked not to be identified because it had not yet been announced. Davis is expected to the sign the contract on Friday.
Davis emerged as one of Houston's top receivers last season when Andre Johnson missed seven games with a knee sprain. Davis finished with 33 catches for 583 yards and three touchdowns. He also returned three kickoffs for touchdowns last season, including two in Houston's season finale against Jacksonville.
Signing Davis was a priority for Houston with the status of one-time Pro Bowl kick returner and restricted free agent Jerome Mathis up in the air. Mathis made the Pro Bowl as a returner in 2005, but spent most of the last two seasons on injured reserve before being charged earlier this month with assaulting his pregnant common-law wife.
A second-round pick in 2002, the 28-year-old Davis revived his career in Houston after finishing with just two catches for 13 yards for Buffalo in 2006. He had three straight 400-plus-yard receiving seasons with the Cleveland Browns, but played mostly special teams in 2005 and 2006 in Buffalo and New England.
A telephone message left by the Associated Press for Kennard McGuire, Davis' agent, was not immediately returned Thursday night.
Davis told Houston television station KRIV the agreement "allows me to really, truly concentrate on football and not worry about the finances."
"I am just extremely excited I am going to be able to be able to continue my career in Houston," Davis said.