The Astros introduced Hinch at a press conference Monday evening at Minute Maid Park.
Houston, which finished the season 70-92 and in fourth place in the American League West, fired Bo Porter earlier this month. The team finished last season with a 51-111 record.
"To know me is to know I like winning. I like to compete. The talent here is evident," said Hinch.
Hinch led the Diamondbacks to an 89-123 record over parts of two seasons. The 40-year-old was fired along with former general manager Josh Byrnes in July 2010.
Hinch has since served in the San Diego Padres' scouting department.
The Astros reportedly interviewed three internal candidates over the weekend: third-base coach Pat Listach, interim manager Tom Lawless and Triple-A manager Tony DeFrancesco.