The three Crimson Tide stars held a news conference on Friday and coach Nick Saban endorsed the move by all three players as "a good business decision."
All-Americans Cooper and Collins are projected as likely top 10 picks, with the receiver widely regarded as one of the top five players available. Yeldon said he received a second-round grade from the NFL's College Advisory Committee, while the other two said they were rated as first-rounders.
Cooper, who is still taking classes this semester, demolished Alabama records with 124 catches for 1,727 yards and 16 touchdowns. The Heisman Trophy finalist who won the Biletnikoff Award as the top receiver said he doesn't worry about the draft projections.
"I just believe it's all speculation," Cooper said. "It really means nothing until it actually happens."
The Tide lost to Ohio State in the College Football Playoffs, falling short of a shot at a second national title for the three players.
"It was a difficult decision with the way that we ended the season, but the more I thought about it, the more I felt like it was the perfect time for me to come out," said Cooper, who indicated he is 20 credit hours from a degree. He had a class shortly after the draft announcement.
Collins was a finalist for the Jim Thorpe Award given to the nation's top defensive back. He had a team-high 103 tackles with three interceptions but like Cooper said falling short of another title left a void.
"I mean, I wanted it as bad as anybody that's playing college right now," Collins said. "It weighed on me, to play one more year and get another chance to run for it again. At the end of the day, you've only got so many years to play football."
Yeldon fell just short of his third straight 1,000-yard season, running for 979 yards and 11 touchdowns while battling hamstring and ankle injuries much of the season. He said he spoke to other Tide running backs who left early, Green Bay's Eddie Lacy and Mark Ingram of the New Orleans Saints.
Yeldon said he was leaving later Friday to train in Palm Beach, Florida. He said he is taking two online courses and is 15 credit hours shy of graduating.
"I worked all my life to get here," Yeldon said. "It was always a dream and a goal. But I got here and I made it. I made the most of the opportunity."
He said Saban talked about the often shorter pro careers of running backs because of the wear and tear on their bodies.
"That's pretty much what he told me," Yeldon said. "Running backs don't get picked that high. They have a short life in the NFL. But that was one of the decisions I made to come out."
Saban's philosophy has been to recommend players leave if they're projected as first-rounders. He said Collins, Cooper and Yeldon all made good calls.
"They have made a good business decision to decide what they want to do with the next year of their football career," Saban said, praising all three players for their character and academic success.
Alabama has had 21 underclassmen leave early counting those three under Saban, including five last year. Defensive tackle Jarran Reed and linebacker Reggie Ragland are among the other draft-eligible juniors.
Asked if any other players were considering leaving, Saban said: "We'll see how it goes."