Meyer was born in Grand Rapids, MI to parents Rita and Jay. He has one older sibling, Matthew Meyer. He met and married fellow runner Paula Lettis in 1980  while living in Boston and together they had three children, Nicolle (1981), Jacob (1983) and Daniel (1986). He divorced in 2005 while living in Dexter, MI.
Meyer resides near Rockford, MI, and since 2008 has served as Associate Vice President for Institutional Advancement at Aquinas College. Previously, Greg was employed from approximately 2000 through March 2007 by the University of Michigan as director of Major Gifts for the Greater Michigan Region, where he helped raise over $125 million for the university.
Meyer's winning time for the 1983 Boston Marathon race was 2:09.00. He was the last American to win the Boston Marathon until 2014. He set ten American Road Racing records and two world records, and won the River Bank Run, in his home town of Grand Rapids, seven times.
"He held the American record for the ten mile run. On the track, he was a sub 4-minute miler (3:58.4), ran 8:26 for the 3,000 meter steeplechase, 13:35.44 for 5,000 meters, and 27:53.1 for the 10,000 meters (1983). Meyer's top-level performances deserve recognition. He set ten American road running records at the following distances: 8K, 10K, 15K, 25K, ten miles. Set two World Records in 1980 & 1981 in the 15K (Gasparilla 15K, Tampa, FL) and the (Cherry Blossom 10 Mile, Washington, D.C.) Some of Meyer's other accomplishments include United States Male Distance Runner of the Year 1983, being nominated for the James E. Sullivan Award (America's highest amateur award) 1983, and being inducted into the following Halls of Fame: ESPN Road Racing, Road Runners Club of American, and Grand Rapids Sports Hall of Fame. He also had victories at the following major races: Detroit Marathon (1980), Chicago Marathon (1982), Boston Marathon (1983), Cascade Run Off (1980), Cherry Blossom (1983), 25K River Bank Run (seven times), and the U.S. National Cross Country Champion (1978). He broke the American indoor 5,000 meter track record with a time of 13:41 at Harvard in 1981. Meyer was one of the founding members of A.R.R.A, which was the first athletic union of road racing athletes. In the early 1980s [he] helped fight [for] and win the right to earn prize money, starting with the Cascade Run Off in 1980. After many runners were banned from running T.A.C. events (now USAT&F) due to the "contamination rule" dealing with professionalism, T.A.C. instituted the TAC Trust system, which eventual lead [sic] to open competition and the prize money the athletes today enjoy…not to mention an open Olympic Games."