Muirhead skippered Britain to gold at the 2022 Winter Olympics in Beijing, adding to bronze from Sochi 2014, and also claimed world and European titles during her career.
“After 15 years of international curling and 21 international titles I have made the hardest decision of my life to hang up my curling shoes and retire," Muirhead said in a post on social media.
“Throughout my career and like most athletes, I have experienced both the highest of the highs and the lowest of lows, and at times the future seemed very distant. It's been an emotional journey, but a journey that I am incredibly proud of.
“Behind every athlete is a team and I have had the opportunity to work with some of the best and therefore there are many thanks to be made. I can't thank everyone here, but will do so individually I hope over the coming weeks."
Muirhead, 32, paid tribute to the support of all of her team-mates “from the bottom of my heart" as well as from the funding received from the National Lottery and UK Sport for the British Curling and Scottish Curling programmes.
“Being skip and representing Team Muirhead, Great Britain and Scotland over the years has been a real honour, and one I have never taken for granted," she added.
“Retiring from curling as a current European, world and Olympic champion is something I always dreamt off, and I am signing off with a huge smile on my face.
“With regards to what's next - I am looking forward to exploring more opportunities and getting my golf clubs out, but watch this space!"
Muirhead, who teamed up with Bobby Lammie to also claim the world mixed doubles crown in April, received an OBE in the Queen's Birthday Honours list earlier this year to add to an MBE from 2020.
Just reaching Beijing itself had capped a remarkable change in fortunes for Muirhead's team, who had looked set to miss out on a place at the Winter Olympics after making a poor start in the final qualification tournament.
British Curling performance director Nigel Holl said: “Eve Muirhead will go down in history not only as one of the greatest ever British curlers, but as one of the greatest sportswomen this country has produced.
“The attitude that has allowed Eve to claim every honour in her sport with a wide array of team mates over four Olympic cycles could not have been better exemplified than in the way she responded to the greatest challenge of her career."
Holl added on the British Curling website: “From the disappointment of missing out on automatic qualification for the Beijing Olympics, she became an integral figure in the re-building process which brought about an extraordinary run of success including winning her third European title on her way to skipping Team GB to gold at the 2022 Winter Olympics.
“It was a turn-around which only the most robust of competitors could have achieved and, as a wonderful ambassador for our sport, she deserves all the tributes that she will most certainly receive on announcing her decision to retire from our sport."
Representing Scotland, Muirhead, born in Perth, won the European Championships three times.
SportScotland chief executive Stewart Harris said: "The impact that Eve Muirhead has had on curling in Scotland is unparalleled.
“Eve's 11 gold medals in Olympic Games, World Championships and European Championships are a true testament to her dedication to curling over the years. Eve is a fantastic role model, through her passion for the sport and her drive to see more people across the country stepping onto a rink and participating in curling."
Additional reporting by PA.