"That is about what we were expecting," said Peters, who came to watch UK's Blue-White Game Saturday. "I am excited with the situation. I am ready to get going already. It's a great situation and getting into the (playing) rotation is definitely on my mind, and I think it is a real possibility.
Peters is the highest UK draftee since defensive end Vincent Burns was a third-round pick in the 2005 draft. That means he went higher than former teammates Myron Pryor, Andre Woodson, Keenan Burton, Jacob Tamme, Wesley Woodyard and others.
"I visited Atlanta last week and knew they were interested with their third-round spot," Peters said. "It was just a matter of things falling in place, and they did. They didn't say a lot to me and I'm really not sure what they liked most, but I am thrilled they picked me.
"I am proud that I came here and got better every year like I said I would. Playing with some of those great teammates I had really helped me, too. It was a great feeling to get close with them and I will remember all of them for a long time."
Peters was with family in Louisville Friday night when he got the call telling him the Falcons would pick him.
"That created a bit of excitement," Peters, who plans to stay in Lexington to get in shape for upcoming mini-camps, said.
Peters was a first-team all-Southeastern Conference selection last year when he had 56 tackles, including 12 for loss and four quarterback sacks. He was SEC Defensive Player of the Week when he had a career-high 10 tackles in a 34-27 win over Georgia and national and SEC lineman of the week when he had seven tackles, including 3.5 for loss and 2.5 quarterback sacks, against South Carolina.
He finished his career with 153 tackles, including 28 for loss, and helped the Cats go to four straight bowl games. Peters has completed his degree in secondary social studies education.