The Kelvan High Command was the ruling body of the Kelvan Armada, the Kelvan military force in the Andromeda Galaxy.

Some time prior to the 23rd century, High Command learned that Andromeda would become lifeless in 10,000 years and it was decided that the Kelvan Empire would need to expand into the Milky Way Galaxy in order to ensure their continued survival. Before sending a significant force, the High Command ordered Commander Rojan and a small team to cross over to the Milky Way Galaxy and report on the situation there, as well as beginning the conquest.

Rojan and his team arrived in the 2260s and made contact with Captain James T. Kirk and the crew of the Federation starship USS Enterprise. After an attempt to return the Enterprise to Andromeda, Rojan and his team began to experience emotions and accepted an offer of aid for their people by the Federation, and accepted resettlement on an uninhabited planet.

After settling on a planet, Rojan dispatched robot probes to Andromeda reporting on all the progress they had made and the offer of assistance that the Federation had made. However, after receiving the initial probe, the High Command ordered that all subsequent robot probes be immediately destroyed. Prefect Tamar proved particularly dilligent in destroying the probes and was "rewarded" with the mission to travel to the Milky Way galaxy to punish Rojan for his traitorous crimes to the Empire. (TOS episode: "By Any Other Name"; TOS - Strange New Worlds 9 short story: "Gone Native")