Iraq had been without a government since former Prime Minister Adel Abdul Mahd resigned in November amid anti-government protests.
Trump spoke with Kadhimi "to congratulate him on his confirmation by the Iraqi Council of Representatives," White House spokesman Judd Deere said in a statement.
"President Trump expressed the support of the United States for Iraq during the ongoing global coronavirus pandemic and emphasized the shared interest with Iraq in achieving the enduring defeat of ISIS," the statement said.
"President Trump also encouraged the Prime Minister to address the Iraqi people's demands for reform and legitimate early national elections," it said.
Iraqi lawmakers approved Kadhimi's government on Wednesday. Just hours later, the United States announced it would grant a 120-day waiver for Iraq to continue importing electricity from Iran. Washington said the move was aimed at supporting the new government.