The Mongol general famed as Genghis Khan’s chief strategist and later serving his successors was Subutai.
Subutai, who lived approximately from 1175 to 1248, was one of the Mongol Empire’s most important commanders. Unlike a khan, he was not a member of the ruling dynasty; his reputation came from operational planning, intelligence, mobility, and the coordination of armies across enormous distances. He served Genghis Khan and later Ögedei Khan.
Subutai directed more than 20 campaigns, including operations against the Jin dynasty and the westward invasion that defeated forces in the Rus' lands and Hungary. His campaigns often used feigned retreats, widely separated columns, and carefully timed converging attacks. The Battle of the Kalka River in 1223 and the battles of Legnica and Mohi in 1241 are especially associated with his strategic career.
Jebe was another major Mongol commander and frequent partner in early campaigns, while Muqali became Genghis Khan’s principal commander in China. Neither, however, is the canonical answer to this question.