Terms of his contract were not disclosed.
Teevens replaces Tyrone Willingham, who stepped down last week to become coach at Notre Dame. Various reports indicated Teevens was a finalist along with Mike Riley, who last week was fired as coach of the NFL's San Diego Chargers.
The 45-year-old Teevens was hired as Dartmouth coach in 1987 by current Stanford Athletic Director Ted Leland.
"Buddy is a man of high integrity and character, a great coach and teacher and a man committed to the highest standard of academic and athletic performance," Leland said.
A Massachusetts native, Teevens has spent the last three seasons at Florida after two years as offensive coordinator at Illinois.
"It is an honor to be part of the Stanford family and I am excited about the opportunity to be the head football coach for one of the finest universities in the country," Teevens said.
Teevens was 10-56 as Tulane coach from 1992-96, but he recruited many of the players responsible for the Green Wave's undefeated season in 1998. He coached at Maine from 1985-86 and at Dartmouth from 1987-91. He also was an assistant at Depauw and Boston University.
"Coach Teevens is a great coach and a great person," said Florida quarterback Rex Grossman, the Heisman Trophy runner-up who worked under Teevens this season. "He's a smart guy and I know the Stanford players are going to love him."
Willingham compiled a 44-36-1 record in seven years at Stanford. The Cardinal won the Pac-10 Conference championship in 1999 and tied for second this past season.
Stanford went 9-3 and concluded the season with a 24-14 loss to Georgia Tech in the inaugural Seattle Bowl. The Cardinal made four bowl appearances under Willingham, but his only win was a 38-0 rout of Michigan State in the 1996 Sun Bowl.
Teevens will have the opportunity to build his own staff. Willingham is taking seven of his assistants to Notre Dame, including defensive coordinator Kent Baer, who was bypassed for the head job with the Cardinal.
Teevens inherits a team that returns quarterback Chris Lewis and wide receiver Teyo Johnson.
Notable deaths of 2014 [PHOTOS]