The 37-year-old was part of the Great Britain crews that won gold in the coxless fours in Beijing and London, before helping the men's eight to victory in Rio last summer.
Triggs-Hodge also won one European and four world titles.
"It's over folks, this old body is hanging up the oar," he said on Twitter. "It's been a blast."
Triggs-Hodge won two of his Olympic and three of his world titles in the the coxless four, an event the British men have now won at five consecutive Olympic Games.
Triggs-Hodge said: "I consider myself extremely lucky to have had the chance to get involved, and had the attributes to succeed, in this wonderful sport.
"Rowing is a world of hard working individuals that thrive in a team environment. I feel fortunate to have been part of such a great community of people who get the best from themselves and encourage the best from those around them.
"With the impending delivery of our second child, the security of an exciting job and the feeling that my body was getting to the end of its athletic life, Rio was a fitting way to complete my Olympic journey and end my career in rowing."
Triggs-Hodge began his international career with a last-place finish as part on the men's eight at the 2004 Athens Olympics, but would go on to claim his first world title as part of the coxless four in Japan the following year.
"Our failure in Athens 2004 seeded an anger and a ruthless desire to prove myself," he added.
"Starting in Oxford in 2005 and culminating with Beijing 2008, this anger was the foundation of my first Olympic gold.
"At London 2012 we proved we weren't a one-hit wonder. Everything changed for Rio 2016 - a year out through illness and a re-positioning within the team, (but) it was the race that delivered so much."
Triple Olympic rowing champion Andrew Triggs-Hodge has retired from international competition.