The former Institute and Glentoran stopper joins the Lurgan Blues on a three-year-deal following a successful loan spell at Ballinamallard United.
Glenavon boss Gary Hamilton told the club website they had been monitoring the 22-year-old for a while and were glad to finally get him on board.
“We’re happy to have signed Rory – he’s a good player and he’s at a good age too," he said.
"He’s young, only being 22, so we can get a lot out of him.
“I’ve been looking at him since he was at Institute, but he was snapped up by Glentoran and got the experience of full time football there.
“He then went out on loan to Ballinamallard at the start of this season, after we tried to sign him then, however Glentoran were looking a fee.
"He signed a pre-contract in January to join us after he returned from loan.
“He’s at the stage where we can get the best out of him using the coaching staff that we have in Johnny and Reggie, who were praised by former keeper Josh Clarke after working with him.”
One player who is heading for the exit door at Mourneview Park though is midfielder Jack O'Mahony.
“We offered a new contract to Jack, which he declined," revealed Hamilton.
"He wanted to look elsewhere, so we wish him all the best for the future.”