Veiel joined the army 1904, and was commissioned as an officer in 1905, serving in the Württemberg cavalry during World War I.

From September 1943 to 20 July 1944, Veiel was Commanding General of Battle Sector V (Wehrkreis V) in Stuttgart.

He was relieved of command because of complicity in the 20 July Conspiracy to assassinate Adolf Hitler.

On 16 April 1945 he was put in the Officer Reserve (Führerreserve) of the Army High Command (Oberkommando des Heeres or OKH).

After World War II, Rudolf Veiel spent two years in American captivity.