Son of a pioneer Dutch-French family, Groesbeck was born in Warren Township near the corner of Mound and Twelve Mile Roads in 1872. His father's election as sheriff in 1880 caused the family to move to Mount Clemens. In 1893 Alex graduated from the University of Michigan
and began a long and distinguished legal career in Detroit. After serving as state attorney general from 1917 to 1920 he became governor for the first of three successive terms in 1921. His Republican administrations were noted for governmental reorganization, prison reform, and expansion of state highways. Highway M-97 was, subsequently, named after him. In 1927 he returned to Detroit, retaining active interest in public affairs until his death in 1953.