The complex was built by Miles Frank Yount, founder of the Yount-Lee Oil Company, who made his fortune during the second Spindletop Oil Boom of 1925.
Named for his daughter, it was completed in 1929 and 1930 for a total cost of $700,000.
The Mediterranean Revival-style three-story apartment building, retail center and garage was named to the National Register of Historic Places in 1978.
In 1999, The Mildred was designated a Texas Historic Landmark.