The 6-9, 218-pound power forward is Coach Tony Barbee's second signee since he took over the program earlier this year.
"I really like Coach Barbee and his whole staff," Cothron tells Inside the Auburn Tigers. "I felt comfortable on my visit there and I like their style of play.
"I also like the new arena and the facilities at Auburn," he adds. "They are really something."
Cothron, who is ranked as the No. 13 power forward in the nation by Scout.com, says he narrowed his choices to Tennessee and UConn prior to signing with the Tigers.
Playing for Flora MacDonald Academy as a senior, the Huntsville, Ala.,, native says he averaged 31 points and 13 rebounds this past season.
"Luke gives us a different level of talent," Barbee said. "He is an immediate difference maker for us along the front line. He is a guy who has the ability to score the ball in a variety of ways inside and outside. He has a knack for being around the ball which makes him a great rebounder.
"We are happy to have Luke join our Auburn Family, but he also fits into the family structure in the things that matter to me in that he wants to be a part of a winner in building something special. He is going to go a long way in helping us reach those goals while at the same time we will help him reach his."
Barbee's other spring signee, 6-7 forward Josh Langford, is a senior at Lee High in Huntsville.
Cothron was identified as one of the nation's top prospects during an impressive junior season at Flora MacDonald. One of his best games came against Quality Education Academy, featuring Kentucky freshman John Wall, in which Cothron scored 41 points and pulled in 19 rebounds.