Just 25 of the chairs will be made available with a white walnut exterior and sandy-coloured leather seat. According to the store, the leather will gain an "elegant patina" over time.
The Eames Lounge Chair made its debut in 1956, and was designed by duo Charles and Ray Eames as a simple and practical piece of furniture.
Vitra put the chair into production in 1959, and it's been consistently popular ever since – becoming one of the most replicated furniture designs of the 20th century.
"It is a particularly important moment to start collecting and using classic furniture like this Eames Chair as the UK government has, at last, made it illegal to sell copies of classic designs," said The Conran Shop founder Sir Terence Conran.
As of 28 January, it is illegal to create, import or sell furniture copies in the UK under legal changes five years in the making.
This new edition of the chair has been produced with the approval of the Eames Office, which oversees and protects Charles and Ray Eames' estate.
Other classic furniture pieces to have been updated recently include Hans J Wegner's Oculus armchair, given a black metal frame, and Verner Panton's plastic Panthella lamp, which now comes in a miniature size.
At the end of 2016, Vitra celebrated the Eames Lounge Chair's 60th anniversary by releasing a new twill-covered edition.
The Conran Shop's edition will be available from 21 March and will retail for £6,465, with each piece sold chronologically as a numbered edition.