Kohli, cricket's biggest global star, has agreed to join the Brown Caps throughout June in a deal that will be seen as one of the biggest coups in recent county history.
News of Kohli's first domestic deal on foreign soil is the latest example of a relaxation in attitude from the Board of Control for Cricket in India.
The BCCI has also allowed Cheteshwar Pujara (Yorkshire), Ishant Sharma (Sussex) and Varun Aaron (Leicestershire) to sign as overseas players in England this year.
The 29-year-old averages more than 50 in all three formats for India and is ranked as the top one-day batsman in the world.
Kohli said: "It has long been an ambition of mine to play county cricket and I am thankful to (director of cricket) Alec Stewart and Surrey for allowing me the opportunity to join them during their 2018 season. I can't wait to get to the Kia Oval."
Former England captain 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.
"At a time when there is much discussion around the future of county cricket, the arrival of Virat should give our domestic game a massive boost and positive exposure around the cricketing world which in turn can benefit every county."
Kohli will be available for three Royal London One-Day Cup games and three Specsavers County Championship fixtures. Surrey are currently 10/1 for the former with Sky Bet.
Surrey's current overseas player, South Africa's Dean Elgar, is contracted to the end of May and they have also strengthened their bowling attacking with recently-retired Proteas seamer Morne Morkel on a Kolpak deal.
A month on the books at Surrey will also hand Kohli the chance to acclimatise to English conditions ahead of India's summer tour.
Kohli averages just 13.40 in his five previous Test appearances on these shores, a drop of exactly 40 on his career mark. In ODIs his average in England sits at 32.33 versus an overall tally of 58.10.
England will host India in three T20s, three ODIs and five Tests from July to September.
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