In 1991, Mikhail Gorbachev removed the constitutional role of the Communist Party. Because of this it allowed non-communists to take power. As a result, Boris Yeltsin then became the first president of Russia.
How did Russian communism end?
In August 1991, communist hardliners and military elites tried to overthrow Gorbachev and stop the failing reforms in a coup, but failed. The turmoil led to the government in Moscow losing most of its influence, and many republics proclaiming independence in the following days and months.
Is there still a Communist Party in Russia?
The Communist Party once was the only party in the Soviet Union. Now the Communist Party of the Russian Federation (КПРФ/KPRF) is one of several parties, but it endures as the second largest party in Russia.