George Sweatt married Evelyn Groomer in late spring of 1921 and soon after began playing for the Kansas City Monarchs in the National Negro League. After George and Evelyn completed their teaching degrees in Pittsburg, they began their careers as teachers in Coffeyville at the Cleveland School. While teaching, George played for the Monarchs. He would return to his teaching job a few weeks after school start and return to the baseball season a few games late. Both his school and the Monarchs gave him leniency to pursue the other.

George played for the Kansas City Monarchs from 1921 to 1925. With the Monarchs he played in the first two Negro Leagues World Series, winning the first. Following the 1925 season, George was traded to the Chicago American Giants, managed by Rube Foster. George and Evelyn moved to Illinois where Evelyn taught and George played baseball full time. Under the Giants, George once again went to the Negro Leagues World Series in 1926 and 1927, the team winning both.

George is the only baseball player to compete in the first four consecutive World Series.