"I am committed to earning my degree in architectural design from Stanford University and am on track to accomplish this at the completion of the spring quarter of 2012," Luck said in a statement.
The school announced Luck wouldn't be made available for comment.
His father, former NFL quarterback Oliver Luck, said: "This is a win-win for him. He gets to spend another year at Stanford, be part of a team that will be highly ranked again next year, finish his degree and enjoy Palo Alto.
"It's not like the NFL is going anywhere, it's one of the best run leagues in the world. It will still be there when he graduates."
The Carolina Panthers own the No. 1 pick in the NFL draft and indicated earlier this week that they would be interested in drafting Luck if he decided to leave school.
Luck's father, who's also the athletic director at West Virginia, said the possibility of an NFL lockout or being selected by the Panthers did not influence his son's decision.
"Call him old school," Oliver Luck said. "He comes from a faction of people who believe you go to college to pursue your degree."
Luck consulted with the Colts' Peyton Manning and the Rams' Sam Bradford before making the decision, ESPN college football analyst Rodney Gilmore reported. Both quarterbacks made similar choices to stay in school.
Luck's decision to stay at Stanford comes as coach Jim Harbaugh is being wooed by NFL teams for a possible job. Harbaugh met Wednesday with officials with the San Francisco 49ers.
He met with Miami Dolphins owner Stephen Ross on Thursday in the Bay Area, two people with knowledge of the situation said. ESPN's Chris Mortensen reported late Thursday that the Dolphins will retain head coach Tony Sparano, according to sources.
New Denver Broncos chief football executive John Elway has said he hopes to interview Harbaugh for their job.
It's unclear whether Luck's decision to stay in school will impact Harbaugh's decision to leave for an NFL job this year. If Harbaugh does leave Stanford, the opportunity to coach Luck next season will likely make Stanford a plum assignment.
Luck was the runner-up this season to Auburn's Cam Newton for the Heisman Trophy and will now be one of the favorites for next year's award.
Luck was widely considered the top draft prospect after two spectacular years at Stanford. His decision will be a blow to the Panthers, who have the No. 1 pick in April's draft and are looking for a quarterback.
Luck capped this season by completing 18 of 23 passes for 287 yards and four touchdowns in the fifth-ranked Cardinal's 40-12 victory over No. 12 Virginia Tech in the Orange Bowl on Monday night.
That helped Stanford (12-1) extend its school record for wins in a season and has the Cardinal poised to finish in the top five of the AP poll for the first time since the unbeaten 1940 team finished No. 2.
Luck is a major reason why Stanford has gone from a one-win team in 2006 before Harbaugh arrived to one of the top teams in the country. He has led Stanford to a 20-5 record in his 25 career starts, missing only last season's Sun Bowl loss to Oklahoma with a broken right index finger.
One of Luck's teammates who won't be back is linebacker Thomas Keiser, who told the Cardinal he intends to forgo his final year of eligibility to enter the draft. He started all 13 games this season and finished with 38 tackles and nine sacks.
Luck has completed 64.4 percent of his passes for 5,913 yards, 45 touchdowns and 12 interceptions in his career. He has also rushed for 807 yards and five scores. That athleticism, along with his strong, accurate arm and on-field poise, has had NFL scouts salivating at his potential as a pro.
Harbaugh, a former star quarterback at Michigan and in the NFL, has called Luck the greatest player he has ever been around.
Luck set school records for TD passes (32), completion percentage (70.7 percent) and passing efficiency (170.2) this season. He is already being mentioned alongside John Elway, Jim Plunkett, John Brodie and Frankie Albert as one of Stanford's great quarterbacks.
Ted Miller covers the Pac-10 for ESPN.com. Information from The Associated Press is included in this report.