During World War II, Bletchley Park housed the Government Code and Cypher School, where Middleton's grandmother, Valerie Glassborow, worked as a code-breaker.
The duchess met with her grandmother's colleague, Lady Marion Body, at the opening and visited with Bletchley Park veterans Peggy Huntington, Joan Joslin, Iris King, and Alma Wightman.
Sir John Scarlett, chairman of the Bletchley Park Trust, welcomed Middleton's presence.
"It was a great honor to welcome the Duchess of Cambridge and to show her where her grandmother worked, especially now that Hut 6, along with other fragile buildings, has been restored to create a permanent and fitting tribute to the thousands of men and women whose work helped to shorten the war."
Bletchley Park was the precursor to today's Government Communications Headquarters (GCHQ).