It charts the British star's move to Hollywood, where he played Igor in Mel Brooks' 1974 film Young Frankenstein.
Feldman rose to fame writing on 1960s shows like radio's Round the Horne, The Frost Report and his own sketch show It's Marty.
The play has been written by Feldman's biographer Robert Ross.
Jones, who was a founding member of the Monty Python team and directed their film The Life of Brian, will direct a four-week season of the theatre production at London's Leicester Square Theatre from 18 January to 20 February.
During the 1960s the Python star worked with Feldman several times, including writing sketches for and appearing in It's Marty.
"When I joined the writing team for The Frost Report, the first person to say 'hello' and make me feel welcome was Marty Feldman," said Jones.
"He was one of those very kind and very funny people who helped all the Pythons along the way.
"It's lovely to be able to say a belated 'thank you' by bringing him back to eye-popping life - sort of! - on the London stage."
Actor David Boyle will play Feldman as he struggles with life in Los Angeles and "comes to terms with the burden of fame he has always craved", as his wife Lauretta "takes to the glamorous lifestyle with alacrity". She will be played by actress Rebecca Vaughan.
Producers say Jeepers Creepers will chart "one of the most powerful and complex partnerships in comedy, through the unique gaze of one of the greatest: Marty Feldman".
The play's writer Ross has penned several comedy biographies, including Feldman, Benny Hill and Carry On star Sid James, as well as The Monty Python Encyclopaedia.
Last year Jones took to the stage himself for 10 Monty Python live shows at London's O2 Arena.
John Cleese, Terry Gilliam, Eric Idle, Jones and Michael Palin appeared together on stage for the first time since 2009. Palin told fans it would be "the last time we'll be working together".
Monty Python's Terry Jones will direct the world premiere of Jeepers Creepers, a play about comedy star Marty Feldman and his ambitious wife, Lauretta.