He was the youngest undisputed chess champion in 1985 after defeating Russian Anatoly Karpov, and played against IBM super-computer Deep Blue in 1996, losing one game, drawing two and winning three.
The 54-year-old has long criticised the Putin regime and was instrumental in setting up The Other Russia, a coalition opposing Putin’s rule.
Kasparov was arrested in Moscow in 2007 after attending a pro-democracy rally and was later beaten and arrested outside the trial of feminist punk band Pussy Riot in 2012.
He told Desert Island Discs that Putin’s actions have been predictable, saying: “It is a one-man dictatorship.
“It was a police state 10 years ago and I’ve been shouting in the desert trying to bring attention to the fact that this regime was on the way to turning into an open dictatorship that would go after other countries.
“That’s what happened with other dictators.
“They destroy the opposition in their own countries so they are in total control.
“But eventually they all need new targets to justify their endless stay in power.
“I knew Putin would go elsewhere.
“First to the neighbouring countries – former Soviet republics – and eventually he would defy the biggest and most powerful countries in the world.”
Kasparov spoke of Russian “interference” in the US and European elections and added: “I’m tired of saying I told you so and I want one day to be proved wrong.”
As a high-profile enemy of the regime he revealed he will only travel to certain countries and won’t have tea with strangers because of the risk to his life.
He says Russians have been conditioned to accept Putin’s rule.
“It is very important to explain the true nature of his regime.
“Many people who were born in the Soviet Union have this genetic fear of expressing their views.
“Speaking of a KGB dictator just goes against their life experience.
“Also if you have only one restaurant in town serving one dish, this dish is popular.”
Kasparov, who lives in New York, confirmed that he intends to keep spreading his anti-Putin message.
Among the discs chosen for his desert island stay were The Godfather Waltz from the 1972 film soundtrack, the Prelude from Bizet’s Carmen, and Mozart’s Symphony No 40.
A telescope was his luxury item.
Desert Island Discs is on BBC Radio 4 today at 11.15am.