Buckley died Wednesday at his home in Stamford, Conn., at the age of 82. A cause of death wasn't immediately known.
Buckley, a prolific writer, lecturer, television host and National Review founder, was "one of the great political thinkers," the president said after a meeting with the special envoy to the Organization of the Islamic Conference.
"He influenced a lot of people, including me," Bush said, adding that he spoke with Buckley's son, Christopher.
"Bill Buckley was one of the great founders of the modern conservative movement. He brought conservative thought into the political mainstream," Bush said in a formal statement released by the White House.
Notable deaths of 2014 [PHOTOS]