The Aldrich Family was launched in its own series as a summer replacement program for Jack Benny in NBC's Sunday night lineup, July 2, 1939, and it stayed there until October 1, 1939, when it moved to Tuesday nights at 8 p.m., sponsored by General Foods's popular gelatin dessert Jell-O, which also sponsored Jack Benny at the time. The Aldriches ran in that slot from October 10, 1939 until May 28, 1940, moving to Thursdays, from July 4, 1940 until July 20, 1944.

After a brief hiatus, the show moved to CBS, running on Fridays from September 1, 1944 until August 30, 1946 with sponsors Grape Nuts and Jell-O before moving back to NBC from September 5, 1946 to June 28, 1951 on Thursdays and, then, as a Sustaining program in its final run of September 21, 1952 to April 19, 1953 on Sundays.Beginning on July 5, 1946, the program ran for 10 weeks on Friday nights as a summer replacement for Kate Smith Sings.

The sponsor, General Foods, used the time to "promote its salt product ... instead of Grape Nuts". The show was a top-ten ratings hit within two years of its birth (in 1941, the show carried a 33.4 Crossley rating, landing it solidly alongside Jack Benny and Bob Hope). Earning $3000 a week, Goldsmith was the highest paid writer in radio, and his show became a prototype for the teen-oriented situation comedies that followed on radio and television.