The 28-year-old centre-half signed for the Hoops today having left Scottish Premier League side, St Johnstone earlier this month.
The Tallaght native who also had spells with Longford Town and Drogheda United explained that he is looking forward to kick-starting his League of Ireland career.
He said: “I am delighted to have signed for Rovers. It’s been a while coming to be honest as I’ve been talking to the club on and off for a while. I am hoping to be part of continuing success at the club.
“I’m really looking forward to getting back into action. I have been a bit frustrated over the last while, not getting to play as much as I’d have liked. I am very hungry to get back playing regularly and I’m happy to have signed for Rovers. There probably isn’t another club in Ireland I’d have come back from Scotland for.
“Living in Jobstown in Tallaght, I went past the stadium over the years and it will be great to get a chance to play there now. It’s an exciting time for me.”
And Stephen Kenny said he is delighted to bring the player to the Hoops.
Kenny said: “Graham is a left-sided centre half so he will bring good balance to our back four. He showed himself to be a good competitor during his time in the league and he will have benefitted from his time at St Johnstone.
“He is from Tallaght and has a strong hunger to do well at Shamrock Rovers and I feel he will make a strong contribution to the club.”