After leading the Inchicore side to the 2013 Airtricity Premier Division title, the 28-year-old centre back joins Trevor Croly in Tallaght
The 28-year-old centre-back played more than 150 matches for the Saints and captained the side to their first League of Ireland title more than a decade.
"This is a new challenge for me and one I'm very much looking forward to," Kenna told the official Shamrock Rovers website. "Obviously I had a good year last season with St Pat’s and it was hard to decide to leave.
"But Shamrock Rovers had approached me two or three times throughout my career and it felt like the right move for me now. I am glad it’s all finalised and we have an exciting challenge ahead of us next season."
Shamrock Rovers have also strengthened this week with the acquisitions of Luke Byrne and Simon Madden.