The 35-year-old forward, whose career was halted for six months after the discovery of an irregular heartbeat in 2016, said in a statement the time was right to draw a line under his playing days.
"After a lot of thought, my family and I have decided that this is the right time for me to step away from the game," said Dempsey.
"I'd like to thank all of the teammates, coaches and support staff that I've worked with throughout my career. It has always been my dream to make it as a pro. I'm grateful to have been on this ride."
Dempsey is one of the most successful US players in history, enjoying spells with English Premier League sides Fulham and Tottenham Hotspur as well as stints in Major League Soccer with New England and Seattle.
At international level, Dempsey scored 57 goals in 141 appearances between 2004 and 2017, putting him level with Landon Donovan as the USA's leading all-time goalscorer.
Dempsey played in the 2006, 2010 and 2014 World Cups, captaining his country in Brazil four years ago when the US reached the knockout phase.
The Texan spent seven years in the Premier League and was fourth in the 2011-2012 Football Writers' Association rankings for Player of the Year after a campaign that included 17 goals for Fulham.
In five years at Craven Cottage, Dempsey scored 50 goals in 184 games, before adding seven goals in 29 appearances for Spurs in 2012-2013.
His Premier League spell saw him become the first American to score a hat-trick in the English top-flight in a 5-2 win over Newcastle in 2012.
Seattle Sounders general manager Garth Lagerwey said Dempsey deserved to be remembered as the greatest player in the history of the American game.
"As far as I'm concerned, Clint Dempsey is the greatest player in the history of our country," Lagerwey said in a statement.
"His mark on both our club and the United States Men's National Team is indelible, and his hard-earned reputation as a trailblazer for our nation in Europe helped pave the way for generations of future of Americans abroad," he added.
United States goalkeeper Tim Howard described Dempsey as "an absolute legend in our game who helped change the perception of what It means to be an American footballer."
"It was an honor to suit up with you and always a challenge to go up against you," Howard wrote on Twitter.