The 36-year-old, who was capped 26 times between 2007 and 2015, has been without a club since leaving his hometown club Dundee at the end of last season.
Adam, who began his career with Rangers and also represented Ross County, St Mirren, Blackpool, Liverpool, Stoke and Reading before enjoying an emotional swansong at Dens Park, has signalled his intention to forge a career in coaching.
On Wednesday, the Dundonian posted a retirement message on Instagram along with a video of some of his career highlights, including footage of the day he signed for Rangers as a teenager.
"I feel now is the right time to announce my retirement as a player," he said.
"I've been lucky enough to play for some of the biggest clubs in the world.
"From Champions League nights at Ibrox for Rangers, winning promotion into the Premier League as Blackpool captain, pulling on the famous Liverpool shirt and scoring in front of The Kop, eight incredible seasons at Stoke City to guiding my boyhood club to promotion and playing 26 times for Scotland - It's not been a bad ride.
"A huge thank you goes to Glasgow Rangers, Ross County, St Mirren, Blackpool, Liverpool, Stoke City, Reading and Dundee's supporters - hopefully I've gave you all some memorable moments along the way.
"For now it's time for me to move into coaching, something I feel incredibly passionate about and have been enjoying for the last few months.
"I'd like to thank my parents, my sister and brothers, my wife Sophie, children Jack, Anabella and Louis and all my family and friends for their support over the last 20 years - couldn't have done any of it without you.
"It's been a pleasure."
Adam had initially been open to extending his stay at Dundee - the club he supported as a child - but he expressed disappointment that the Dark Blues were unable to offer him a new contract following their relegation from the Scottish Premiership at the end of last season.