Former England batsman Solanki, who finished his playing career with Surrey before joining their backroom staff, succeeds Australia’s Michael Di Venuto at the London-based club.
He is set to start his new post next week when group training resumes. The coronavirus pandemic has delayed the start of the English domestic season until August at the earliest.
Last year Solanki worked with star batsman Kohli when an assistant coach under former India boss Gary Kirsten at the Royal Challengers Bangalore in the IPL.
The 44-year-old, whose Surrey squad contains several England internationals including Rory Burns, Ollie Pope, Ben Foakes and the Curran brothers, said his experience with Kohli had showed him how top players deal with pressure.
“Just to see how people react to pressure situations, the likes of Virat… gave me an insight into the superstars of the game,” he said.
Solanki, born in India, but brought up in England, is believed to be the first British Asian head coach of a first-class county.
The worldwide Black Lives Matter protests sparked by the death of George Floyd in the United States has led to a debate about the lack of non-white players and coaches in English cricket.
Solanki started his career being coached at Worcestershire by Basil D’Oliveira.
The former Test batsman was rejected by the apartheid government of his native South Africa for an England tour in 1968 because he was classified as “Cape Coloured” – an incident that contributed to South Africa’s decades of sporting isolation.
Solanki said he was unsure if his promotion constituted a “watershed moment”, saying while he abhorred racism and felt sympathy for anyone discriminated against, it had not been an issue in his career.
“There certainly is a great degree of movement throughout the world,” said Solanki, who made 54 limited-overs international appearances for England.
Solanki, however, was at a loss to explain why he was believed to be the first British Asian head coach at one of England’s 18 first-class counties.
“I couldn’t possibly answer that. I’ve not been party to any of the decisions that appoint coaches. I couldn’t tell you.
“But at Surrey, with the numerous programmes to encourage involvement of people from different backgrounds, I consider it as something that’s ongoing.
“If this (his appointment) accelerates all those matters, then great.”