Peters was born in Wesel, North Rhine-Westphalia, Germany. He began riding at age seven, and competing in weekend dressage shows. By 15, he was competing outside of Germany, at international competitions in Belgium and Denmark. He received his first horse, Udon, at age 16 as a gift from his father; this horse would carry him to a bronze medal in the 1996 Summer Olympics. In 1984, he spent the summer training in San Diego, California, before returning to Germany to perform his army service. In 1985, he returned to the United States with Udon. In 1991, he opened his own barn and acquired his first sponsor, Lila Kommerstad, who purchased Udon and as of 2012 owned a portion of Peters' Arroyo Del Mar training barn. Peters gained his US citizenship in 1992, saying, "The whole idea of being so patriotic, of feeling so close to one's country makes a difference. There are not too many other countries where the people are so patriotic. I really enjoy this about America." Peters continues to live in the San Diego area with his wife, Shannon. Their large dressage barn is home to approximately 65 horses as of 2012, around half of which the couple trains and the other half of which are in training under other riders. Outside of his competition and training schedule, he teaches in around 30 training seminars each year. His staff call him "a machine" with regard to his training and competition schedule, and in addition to riding, he participates in swimming, cycling and tennis.
Peters' show record before the 1992 Summer Olympics made him a hopeful to compete for the US team. However, his citizenship papers were not processed in time to compete in the Olympic trials, and so he did not compete in Barcelona. Peters won his first Olympic medal when he rode with the US dressage team to a bronze medal at the 1996 Summer Olympics in Atlanta, together with Robert Dover, Michelle Gibson and Guenter Seidel. Peters, riding Floriano, was an alternate for the US team at the 2004 Summer Olympics, and did not compete. In 2006, with an aging Floriano, Peters and the US team won bronze at the 2006 World Equestrian Games. Soon after, he began riding TC Ravel, who would become his most successful horse. Despite being gelded while in quarantine after his shipment from the Netherlands and suffering an injury in 2007 that prevented training, Ravel carried Peters to a qualification for the 2008 Summer Olympics. In individual dressage competition at the Games, Peters placed fourth, riding Ravel. The US team finished fourth at the 2008 Games, but was disqualified after team member Courtney King's horse tested positive for felbinac, a banned substance. In 2009, Peters and Ravel had the highest scores in all three portions of the prestigious German Aachen World Equestrian Festival Grand Prix competition, leading them to be the first American pair to be named the Aachen Grand Prix Champions.
Ravel and Peters went on to win the 2009 World Cup Final, two bronze medals in individual competition at the 2010 World Equestrian Games, and be twice named the US Grand Prix Dressage Champions. In 2009, The Chronicle of the Horse named Peters and Ravel Horse and Horseman of the Year, and the United States Equestrian Federation (USEF) named Ravel as Horse of the Year. At the time, the Chronicle called him a "natural athlete with a balanced seat and an inherent understanding of the horse. He's calm under pressure and has a reputation for having ice water in his veins." In 2011, riding Weltino's Magic, he took gold in both the team and individual dressage events at the 2011 Pan Am Games. At the 2012 Summer Olympics he came 17th in the individual dressage and was part of the US team which came 6th, again riding Ravel. Peters retired Ravel from competition after the 2012 Olympic Games, after over 40 Grand Prix wins, and the same year the horse was inducted into the United States Dressage Federation Hall of Fame.
Following Ravel's retirement, Legolas became Peter's main competition horse. The pair went on to compete at the 2014 World Equestrian Games in Normandy, France. Peters placed 10th in both of the individual events and 4th in the team dressage competition. At the beginning of 2015, he participated at the Dressage World Cup finals in Las Vegas. Peters was however eliminated because of a blood on Legolas' side. Later that year he participated at the 2015 Pan Am Games, where he successfully defended both of his gold medals from 2011.
As of 2017, Peters' main international competition horse is Rosamunde.