India cricket captain
Kohli's participation in county cricket means he will be unavailable for India as they take on Afghanistan in a Test match in June in Bengaluru.
"It has long been an ambition of mine to play county cricket and I am thankful to Alec Stewart and Surrey for allowing me the opportunity to join them during their 2018 season," Kohli told the club's website.
"I can't wait to get to the Kia Oval."
Surrey's director of cricket Alec Stewart said: "We are thrilled to have signed the biggest name in world cricket for the month of June.
"Playing and training alongside Virat will be a massive benefit for our players who will have the opportunity to learn so much from him."
India begin their tour of England in July with three Twenty20 internationals and three one-day internationals. They then take on the hosts in a five-test series starting in August.
Surrey have also been linked with signing banned Australia pair David Warner and Steve Smith.
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