Luck, who finished second to Griffin in last year's Heisman Trophy balloting, went first to the Indianapolis Colts and Griffin was chosen second by the Washington Redskins.
Those two teams had already announced they would take the players they eventually selected, quarterbacks who had for months been the faces of the 2012 draft.
After the names of Luck and Griffin were announced, the first round of the draft turned surprising with major trades involving three of the first six selections.
Luck, from Stanford, and Griffin, the first Heisman Trophy winner ever from Baylor, became the first quarterbacks to go 1-2 in the draft in 13 years.
Luck, who likely would have been the No. 1 pick if he had chosen to enter the draft last year, returned to Stanford for his senior season and became that school's all-time leader in touchdown passes, completion percentage and total offense.
He will take over for Peyton Manning, whose rewriting of the NFL record book was put on hold in 2011 by a neck injury that cost him an entire season. Manning and the Colts then parted company and he wound up signing as a free agent with Denver.
Griffin threw for 4,293 yards and 37 touchdowns during his final collegiate season and became one of just four players in major college football history with at least 9,000 passing yards and 2,000 rushing yards in his career.
After Luck and Griffin were chosen, Cleveland moved up one spot to No. 3 and selected Alabama running back Trent Richardson. In addition to giving up the fourth pick to Minnesota, the Browns gave away picks in the fourth, fifth and seventh rounds.
The Vikings then took offensive tackle Matt Kalil from Southern California.
Jacksonville next jumped up two positions in a trade with Tampa Bay to choose wide receiver Justin Blackmon of Oklahoma State and Dallas worked a deal with St. Louis for the sixth spot and selected LSU cornerback Morris Claiborne.
The rest of the Top 10 choices in the first round were safety Mark Barron of Alabama to Tampa Bay, quarterback Ryan Tannehill of Texas A&M to Miami, linebacker Luke Kuechly of Boston College to Carolina and cornerback Stephon Gilmore of South Carolina to Buffalo.
The pass-minded nature of the NFL was reflected in the first-round selections Thursday, with only one running back taken among the first 30 picks. Four quarterbacks were chosen and 21 of the 32 picks were from the defensive side of the ball.
Defending NCAA champion Alabama had four players taken in the first round. In addition to Richardson and Barron, the Crimson Tide sent cornerback Dre Kirkpatrick to Cincinnati with the 17th pick and linebacker Dont'a Hightower to New England with the 25th choice.
After Luck, Griffin and Tannehill, the fourth quarterback chosen was 29-year-old Brandon Weeden of Oklahoma State. He was drafted No. 22 by Cleveland.
Eight of the first-round picks changed hands before the selections were made.
Celebrity Families of 2014 [PHOTOS]