Upon graduation from the United States Military Academy in 1951 he was commissioned a second lieutenant and attended the U.S. Army Infantry School at Fort Benning.

Meyer's first assignment was as a platoon leader in Company C, 25th Armored Infantry Battalion in the Korean War from 1951 to 1952.

[1] He graduated from the Armed Forces Staff College in 1964, receiving a promotion to temporary lieutenant colonel in May 1964 and permanent major in June 1965.

[1] Returning stateside, he graduated from the National War College in 1967, then served in the Plans and Operations Division, Office of the Joint Chiefs of Staff until 1969, promoted to temporary colonel in November 1968.

[2] During his tenure he prosecuted an Army-wide modernization program with emphasis on quality over quantity, stressed the need for a long-term investment in land force materiel, and launched a unit-manning system to reduce personnel turbulence and to enhance readiness.

Meyer was responsible for many improvements which transformed the US Army from having poor morale and discipline in the 1970s to a far more professional and capable force in the 1980s.

His son, Tom, is a political cartoonist who is married to Gretchen Nash and has a daughter named Mia.