Nicknamed "White Wings" for his speed,[citation needed] he also totaled 228 stolen bases, 623 hits, 96 doubles, 54 triples, and 441 runs scored.

The older brother of infielder Patsy Tebeau, who was his teammate while in Cleveland, George played over 50 games at all three outfield positions and first base.

He later became the owner of the Kansas City Blues franchise of the American Association.

In addition, Tebeau is recognized as the joint-first Major League Baseball player ever to hit a home run in the first at-bat of his career.

He shares this "first ever" distinction with Mike Griffin; both Tebeau and Griffin hit their debut at-bat home runs on the same day, and as it is unclear which player hit his home run at a chronologically earlier time of the day, both have historically been considered the "first."