The museum was founded in 1816 with the bequest of the library and art collection of Richard, VIIth Viscount Fitzwilliam of Merrion. The bequest also included £100,000 "to cause to be erected a good substantial museum repository". The "Founder's Building" itself was designed by George Basevi, completed by C. R. Cockerell and opened in 1848; the entrance hall is by Edward Middleton Barry and was completed in 1875.
The museum has five departments - Antiquities; Applied Arts; Coins and Medals; Manuscripts and Printed Books; and Paintings, Drawings and Prints.
The "Friends of the Fitzwilliam" was founded in 1909 and is the oldest society in Britain devoted to supporting a museum.