The 33-year-old defender, who moved across the Black Isle from Inverness Caledonian Thistle in 2011, brings the curtain down on a 15-year career in the Highlands.
Munro featured in six of County's nine Premiership games this season, and manager Derek Adams said: "Grant had a terrific two years with the club winning the First Division Championship and finishing fifth in the SPL last season. He goes with our club's best wishes."
Munro made over 300 appearances for Caley Thistle over 11 seasons before his switch to Dingwall. He admits that the thought of not playing as regularly as before had influenced his decision.
He told Moray Firth Radio: "When you reach 30, your toughts turn to the end of your career and the next stage in your life.
"I asked the manager if my time was up and we both came to the agreement. He didn't want to stand in my way if that's how I felt, so credit to the club for getting things done so quickly.
"Everyone knows when it's time for change. I wasn't going to play as much as I wanted to. I need to go into the world now and the next part of my career.
"I wasn't going to go beyond next summer in any case so it gives me a few months' head start going into a new career."