Murray became the first Briton in 77 years to win the title at Wimbledon, against world number one Novak Djokovic. Murray's win came nearly eight decades after Fred Perry won his last of three titles at The Championships.
The Scot's outfit will be displayed in the 2013 Championships showcase. Visitors can see the full winning kit, as well as other autographed items belonging to him.
Also included in the showcase are dresses worn in the women's final by Champion Marion Bartoli and finalist Sabine Lisicki.
Ashley Jones, the museum's commercial manager said: "We are thrilled. The display doesn't fail to conjure up emotions, taking you back to the celebrated moment history was made – we're delighted we can extend this stirring experience to visitors the world over. It is truly a winning display."
The museum recounts the history of the game of tennis, of the Wimbledon Club and The Championships as well as the state of the current game and champions of today.
It also aims to provide inspiration to people following in Murray's footsteps.
Guests on guided courts can take in views of London from the picnic terraces; see where the action happens on Centre Court and explore other exciting areas of interest normally unseen by the public.
Meanwhile, Royal Mail is to mark Andy Murray's historic victory in the Wimbledon men's tennis final with a special set of stamps.
The issue, on sale from August 8, will consist of four stamps featuring different images, all printed within a miniature sheet, costing £3.76.
Two stamps show the Scot with the trophy (one at first class rate and one at the £1.28 overseas letter rate) and two are action shots from the final (one at first class rate and one at the £1.28 overseas letter rate).
Andrew Hammond, managing director, stamps and collectibles at Royal Mail, said: "We are thrilled for Andy and are delighted to mark his wonderful achievement by issuing a set of special stamps. His historic win at Wimbledon has made the nation proud, and we can now celebrate his success with this new stamp issue.
"Andy's stamp joins just a handful of special stamps we have issued to mark unique moments in British sporting history, including the next day gold medal stamps for London 2012, England's Ashes and football and rugby World Cup wins."
This is the second time Murray's achievements have been marked by a Royal Mail stamp.
A gold medal stamp was issued to mark his win in the men's singles at the London 2012 Olympic Games last summer.