The call will take place on Saturday, both the U.S. official and Kremlin spokesman Dmitry Peskov confirmed on Friday.
"As it usually happens during such contacts, the sides will naturally exchange opinions on key parameters of the current state of bilateral affairs," Peskov told reporters Friday. "One can hardly expect substantive contacts on the entire range of affairs from this call ... Let us wait and see, let us be patient."
During an interview with Fox News that aired Thursday night, Trump said of Putin, "He called me after I won, but I haven't had a discussion, but I understand we will be having a discussion soon."
The announcement comes just two days after Peskov had said a call was not scheduled yet. "No one is jumping the gun because we realize that they, Washington, need time to settle down," Peskov said Wednesday.
Trump and Putin did speak after the election on Nov. 14, in what was described merely as a congratulatory call.
Then in December, Trump shared a "very nice" letter he received from the Russian leader, who wrote, "I hope that after you assume the position of the President of the United States of America, we will be able -- by acting in a constructive and pragmatic manner -- to take real steps to restore the framework of bilateral cooperation in different areas as well as bring our level of collaboration on the international scene to a qualitatively new level."
White House press secretary Sean Spicer tweeted Friday morning that President Trump will also speak by phone with French and German leaders on Saturday.
Trump has criticized German Chancellor Angela Merkel's migration policies, saying in a Jan. 15 interview with Times of London that Merkel made a "catastrophic mistake" by allowing 1 million migrants to enter her country.
French President Francois Hollande said in a joint news conference with Merkel on Friday in Berlin that a Trump administration is a "challenge for Europe."
National elections are being held this year in France and Germany. Merkel is running for her fourth term while Hollande has said he will not seek reelection.
Trump is hosting British Prime Minister Theresa May Friday at the White House.
ABC News' Devin Dwyer, Katherine Faulders, Dragana Jovanovic, Kirit Radia and Tanya Stukalova contributed to this report.