The question of the precise relationship between Ronald Reagan's two-term presidency and the end of the Cold War is being hotly debated as I type. David Kaplan, writing in Slate, concludes that though he is responsible, it's more indirectly and more collaboratively than his hagiographers would have it:
Reagan the well-known superhawk and Reagan the lesser-known nuclear abolitionist are both responsible for the end of [the Cold War]—along with his vital collaborator Mikhail Gorbachev.
The Gorbachev factor—too often overlooked in this week of Reagan-hagiography—was crucial. If Yuri Andropov's kidneys hadn't given out, or if Konstantin Chernenko had lived a few years longer, Reagan's bluster and passion would have come to naught; the Cold War would probably have raged on for years; indeed, Reagan's rhetoric and actions might have aggravated tensions.
[. . .]
In the end, Reagan and Gorbachev needed each other. Gorbachev needed to move swiftly if his reforms were to take hold. Reagan exerted the pressure that forced him to move swiftly and offered the rewards that made his foes and skeptics in the Politburo think the cutbacks might be worth it.