Mallett, who is the front-runner to start for Houston next season, signed a two-year extension worth $7 million, with $1.75 guaranteed.
He was acquired in a trade from New England in August and started twice in three appearances for Houston before tearing a pectoral muscle and missing the rest of the season.
Mallett wanted to return to Houston and is eager to compete for the starting job. He's still recovering from surgery on his torn pectoral muscle, but should be healthy soon and ready to vie with Ryan Fitzpatrick and Tom Savage to start for the Texans.
Tarpinian has appeared in 22 games with three starts for Houston since he was signed in 2013.