How did Ronald Reagan and George H.W. Bush's presidencies end the Cold War in the United States' favor?

Reagan's role in ending the Cold War was to ramp up U.S. military spending with the hope that the Soviet Union could not keep up. His Strategic Defense Initiative, derisively called "Star Wars" in the American press, intimidated the Soviet Union into scaling back their nuclear arsenal. Reagan also supported anti-Soviet rebellions behind the Iron Curtain, and the US backed the Solidarity movement in Poland. Reagan broke away from the detente arrangement held by the Nixon, Ford, and Carter administrations because he said America was prolonging the war by not being confrontational.
George H.W. Bush opened friendly negotiations with the Soviet premier Mikhail Gorbachev. Bush also helped oversee the reunification of Germany and the fall of the Berlin Wall. In 1991, America and the Soviet Union signed the Strategic Arms Reduction Treaty. Within a year, Ukraine and Belarus, traditionally part of the Soviet Union and the Russian empire, declared their independence and the Soviet Union ceased to exist.  
http://reagan.civiced.org/lessons/middle-school/presidential-leadership-cold-war

https://millercenter.org/president/bush/foreign-affairs