McKenna made his North End debut in 1997 and scored 32 times in 476 games for the Lilywhites, placing him fourth on the club's all-time appearance list.
At Forest, McKenna will be reunited with former Preston boss Billy Davies.
Irvine told the club website: "Paul McKenna has been a fantastic servant for this club. We cannot criticise him in any way for deciding to join Nottingham Forest at this time. I don't think anyone could feel that Paul hadn't given everything for this club and been very loyal.
"His record is phenomenal and anyone who could play more games than Sir Tom Finney for Preston has obviously been a fantastic player for this club. It was very difficult to stand in his way once Forest came up with what we thought was the right sort of figure.
"He's been a model professional. The whole time I have been here he has been fantastic on and off the pitch and that continued right up until the day he left. I wish him well and I hope that Preston North End fans feel the same."