The peach outfit will form part of the V&A's You Say You Want a Revolution? Records and Rebels 1966-70 exhibition.
Opening in September, it aims to explore the impact of the late 1960s counterculture upon the present day.
Other items in the show include a piece of moon rock, a rare Apple 1 computer and shards from Jimi Hendrix's guitar.
The exhibition has been put together by Victoria Broackes and Geoffrey Marsh, who also co-curated the V&A's blockbuster David Bowie exhibition in 2013.
It will focus on the places and events - such as London's Carnaby Street and UFO Club, the Paris protests of May 1968 and the Woodstock Festival of 1969 - that helped define the period.
Harrison's suit is being loaned by his widow, Olivia, along with the musician's sitar, letters and a diary about the recording of the Sgt Pepper's Lonely Hearts Club album, which was released in 1967.
Ms Broackes recalled the moment she was shown the suit for the first time. "It was put on a table and looked beautiful - it had a hat with a feather and special cuffs. To see the whole thing laid out together is incredibly exciting."
Other Beatles items on display include John Lennon's lime green Sgt Pepper outfit - which has been on display previously - and handwritten lyrics for Lucy in the Sky with Diamonds.
The exhibition's launch event took place at The Bag O'Nails club in London's Soho where The Beatles and The Jimi Hendrix Experience played, and where Sir Paul McCartney met his future wife Linda Eastman in 1967.
Martin Roth, director of the V&A, said: "There is nothing about our lives today that wasn't affected by the political and social changes that happened then."
Among the 350 objects on show will be:
The V&A is also borrowing more than 200 LPs from the collection of the late BBC broadcaster John Peel which will "form the spine of the exhibition".
Special headsets worn by visitors will provide an audio guide which changes the sound according to the visitor's position in the gallery.
"The exhibition is about much more than music but it is music that carries the story," Ms Broackes said.
You Say You Want a Revolution? Records and Rebels 1966-70 is at the V&A 10 September 2016 - 26 February 2017.
The original suit worn by George Harrison on the cover of The Beatles' Sgt Pepper album is to go on public display for the first time.