The Lounge Chair Twill and matching Ottoman will be available for a limited period of three months between November 2016 and January 2017.
The company hopes the black fabric – which is complemented by warm reddish tones of palisander wood in the frame – creates a "cosy softness and inviting warmth".
While the armchair has been released with a few variations in the past, Vitra has always produced it exclusively in leather.
The newly upholstered models will also come with a corresponding label acknowledging the anniversary, along with a celebratory "60 years in Production" certificate.
Designed in 1956, the chair was originally conceived by American designer duo Charles and Ray Eames as a simple, practical and comfortable piece of furniture.
Vitra first started producing the chair, now an icon of mid-century modern design, in 1959. Due to its enormous popularity, it has become one of the most replicated furniture designs of the 20th century.
"[The Eameses] set new standards with their novel interpretation of the classic club chair: their model was light, elegant, modern and comfortable," said Vitra.
"With its functional perfection and careful construction, timeless materials and balanced proportions, the Lounge Chair has established itself over its 60-year history as one of the most significant classics – as a product from another era that remains as relevant as ever."
Vitra has been manufacturing Eames furniture since 1957 and now holds the rights to the designs in Europe and the Middle East. It recently also adapted the Eames wire chair, giving it a powder coating suitable for outdoor use.