Radev has however stressed that he is committed to Bulgaria remaining a member of the EU
"The crisis between NATO and the European Union on one side and Russia (on the other) is clear. More confrontation will not help its resolution. The Cold War is a sad experience of the past," said Rumen Radev.
"The US presidential election result and the new political climate in the world give hope that dialogue will resume soon," Radev, due to be inaugurated on Sunday, two days after Trump, told parliament.
Radev, 53, a former air force commander and partially US-trained fighter pilot backed by the opposition Socialists, was elected to ex-communist Bulgaria's largely ceremonial presidency on November 13.
During his election campaign Radev called for EU sanctions on Russia to be lifted and said that Crimea, annexed by Moscow in 2014, is "de facto Russian".
Russian President Vladimir Putin in November welcomed his victory and said he hoped for a "new impetus" in relations between the countries' "brotherly peoples".
Radev has however stressed that he is committed to Bulgaria remaining a member of the EU, calling Thursday for the bloc to stay unified "at all costs".
His election also prompted centre-right premier Boyko Borisov and his government to resign. Fresh elections are set to take place in the EU's poorest country in late March.
Radev, who has no previous political experience, is expected to dissolve parliament next week, announce the election date and appoint a technocrat government.