O'Conner went to Tampa Bay 14 picks after the club selected prep outfielder Josh Sale with their first selection on Monday and 11 picks before it selected prep outfielder Drew Vettleson with the 42nd pick.
"I'm actually ecstatic right now," O'Conner said. "... This is like a dream come true. It's what I've always wanted to do. Really, really happy right now."
The Rays received the 31st pick as compensation for not being able to sign LeVon Washington, last year's No. 1 pick and the 30th overall pick of the Draft.
O'Conner, 18, is listed on the Draft board as a catcher, shortstop and pitcher. But the Rays are looking at him at catcher.
"I'd say I'm pretty raw right now [as a catcher]," O'Conner said. "I haven't really had any work there or anybody to really work with me. I'm comfortable back there. ... I feel more and more comfortable every time I get back there."
O'Conner began catching last summer and caught regularly this spring after playing shortstop, third base and pitcher earlier in his career. As a junior, he was named an AFLAC All-American and won the metal-bat home run derby at the Perfect Game National Showcase in Minneapolis. He was the top-rated prospect out of Indiana.
"He is essentially a high school shortstop who started catching this year," Rays scouting director R.J. Harrison said. "So what you have is you have a kid with a plus arm, plus raw power, and we think he's going to be able to make that transition to catcher.
"... We don't think it's going to be a tough transition for him. He's a kid who wants to catch."
O'Conner is the first catcher selected by the Rays in the first round. He is said to be a hard worker with ability. He has an easy and efficient right-handed swing along with a good body frame that can support some solid growth.
He hit .470 with eight home runs and 40 RBIs in 66 at-bats, with 15 stolen bases his senior season.
While he has committed to play baseball at the University of Arkansas, it doesn't look like he'll head for Little Rock. Rays executive vice president of baseball operations Andrew Friedman said the organization has already reached an agreement in principal with O'Conner.