Golson graduated this semester, allowing him to transfer and play his final season at a new school without sitting out a year.
"I would like to thank everyone at Notre Dame for the opportunity to compete at the highest level of college football but most importantly to obtain my degree from one of the finest universities in the country," Golson said in a prepared statement. "To all the Fighting Irish fans I want to thank you for the support over the past four years and let you know I truly love Notre Dame! To my former teammates, who I will miss tremendously, I wish much success in the future and will be your biggest fan from afar."
A 6-foot senior, Golson is undecided where he will transfer, a source said. Schools that might be interested in Golson include Alabama, Florida, Florida State, LSU and Texas.
"I will have no future comment at this time and ask that you respect my time as I figure out this life changing moment," Golson said. "God has a plan for each of us and I ask for your prayers as I move forward in this new journey in my life."
If Golson wants to transfer to an SEC school, he would require a waiver that has been approved by the league commissioner, an SEC source said.
"A waiver is possible, but not easily granted," a source said.
The SEC's graduate transfer rule -- 184.108.40.206 -- states the student-athlete must meet seven criteria. Golson would not meet the fourth criteria, 220.127.116.11d, which states: "The student-athlete has not been subject to official university or athletics department disciplinary action at any time during enrollment at any previous collegiate institution [excluding limited discipline applied by a sports team]."
Golson did not play during the 2013 season after he was suspended from Notre Dame for "poor academic judgment" and was not enrolled in the school. He returned to Notre Dame before the 2014 season.
In January, a source told ESPN that about "two dozen schools," including six SEC schools, were interested in Golson if he left Notre Dame.
This spring, Fighting Irish coach Brian Kelly had said repeatedly he expected Golson to return for his senior season. Golson was battling junior Malik Zaire for the starting spot.
Michael Bertsch, Notre Dame's director of football media relations, tweeted a statement from Kelly.
Golson started 23 of 25 games in his Notre Dame career but did not start the Irish's Music City Bowl victory against LSU. Zaire started the game, with Golson coming off the bench in the second quarter.
In two seasons at Notre Dame, Golson threw for 5,850 yards, 41 touchdowns and 20 interceptions. In 2012, he led Notre Dame to an undefeated regular season, after which it lost to Alabama in the BCS title game.
Last year Golson led the Irish to a 6-0 start before they lost at Florida State on a last-minute offensive pass interference call. The Irish then dropped five of their next six games with Golson finishing with 22 turnovers on the season.
In the regular-season finale against USC, Golson was benched in the 49-14 loss.
After the bowl game and all spring, Kelly said he would hold a competition to determine a starter for the 2015 season.
"The decision on playing time will take care of itself," Kelly said after the spring game last month. "They can't control that. All they can control is what's in their purview and that is the fundamentals of what we've asked them to work on, and the rest they can't really worry about. It's not their call."
"In terms of depth," Kelly said, "I don't know if anybody has a better situation than we do in terms of the two quarterbacks we have."
After Golson's departure, Kelly must now find another quarterback if he's to have that same depth.