The Astros announced the move at baseball's winter meetings. Luhnow takes over for Ed Wade, fired along with team president Tal Smith last month in the first major changes by new owner Jim Crane.
The 45-year-old Luhnow had been a vice president with the St. Louis Cardinals since 2003. He has overseen the Cardinals' drafts for several years and was involved in selecting several players who contributed to their World Series championship this year, including Jaime Garcia, Allen Craig, Jon Jay and Lance Lynn.
In 2006, Luhnow added player development to his duties. Cardinals farm teams have won five minor league championships since then.
"Jeff is the perfect fit for the Astros because of his track record in scouting and player development during his eight-plus seasons with the Cardinals," Astros president and chief executive officer George Postolos said in a statement.
The Astros became the seventh of the 30 major league teams to hire a new general manager or head of baseball operations since the end of the season. Other clubs that changed recently were Baltimore (Dan Duquette for Andy MacPhail), Boston (Ben Cherington for Theo Epstein), the Chicago Cubs (Jed Hoyer for Jim Hendry), the Los Angeles Angels (Jerry Dipoto for Tony Reagins), Minnesota (Terry Ryan for Bill Smith) and San Diego (Josh Byrnes for Hoyer).
Houston went 56-106 last season, the worst record in franchise history.
Luhnow has been in charge of the Cardinals' Latin American scouting and development since 2004. He has been credited with developing players from the area who have reached the majors as well as become top prospects in the minor leagues.
"The Astros strive to develop one of the best systems in baseball and create a consistent winner at the Major League level," Postolos said. "Jeff has the knowledge, skills and experience to lead the baseball operations efforts at all levels and help the Astros achieve this vision. Jeff has demonstrated the ability to inspire and motivate staff in the front office and out in the field."
Baseball owners approved the sale of the Astros from Drayton McLane to Crane on Nov. 17, a transaction that requires the franchise to move from the NL Central to the AL West in 2013. The sale was officially completed on Nov. 22 and Crane fired Wade the next day, a move the team didn't announce until Nov. 27.