The veteran midfielders scored the goals that guaranteed County's top-flight status thanks to a 2-1 win at Motherwell on the final day of the Scottish Premiership season.
Callum Morris, Jason Naismith, Ross Draper, Billy McKay, Jermaine Hylton, Mohamed Maouche, Carl Tremarco and Tony Andreu are also being released by the Dingwall club following the appointment of Malky Mackay as manager on Wednesday.
Keith Watson, Blair Spittal and Ross Munro are in talks over new contracts.
Gardyne, 35, has signed for County four times and is the club's record goalscorer and appearance holder, and has won seven trophies during more than 11 years of service.
A club statement read: "Over those years Michael has been an incredible servant of the club, become a friend to many and will always have a special place here at our club."
Club captain Vigurs, 33, has had two spells with both County and Inverness.
"Iain has built a great connection with our club over the years and will always be held in high regard for his contributions to where the club is today," the statement added.
"Both Michael and Iain were instrumental in the club achieving the success it has - particularly the 2010 Scottish Cup final run, our 40-match unbeaten run to take us to the Premiership for the first time in our history and Michael in our 2016 Scottish League Cup triumph."