The call lasted 30 minutes and was the first conversation Moon Jae-in had with a world leader since his inauguration on Wednesday, Yonhap reported.
Trump told Moon the strong bilateral alliance defended the two countries against North Korea, then invited the newly elected South Korean president for a state visit, Voice of America reported.
Moon said the alliance with Washington is his top priority.
"In current circumstances where there is growing uncertainty on the Korean peninsula and the region, the U.S.-South Korea alliance is more important than ever before," Moon said, according to Yonhap. "The U.S.-South Korea alliance is the foundation of our foreign policy, and will continue to be so."
Trump said the relationship is not simply good, but great, and that their two presidential election victories should be celebrated together, according to the report.
But differing viewpoints may soon surface between the two leaders.
Moon has said he would "go to Pyongyang if conditions are met" during his inaugural address, and had proposed the reopening of a jointly operated factory park in the right circumstances.
Some of those goals would collide with those of the Trump administration, which is seeking to place more economic sanctions on North Korea to pressure Pyongyang to give up its nuclear weapons.
Moon and Trump may also disagree on the U.S. missile defense system THAAD.
Trump had said Seoul should pay $1 billion for the system, which has already been deployed, but Moon had said the deployment should be scrutinized or reviewed.
Moon also called China's Xi Jinping on Wednesday and spoke to the Chinese leader for 40 minutes.
The phone call went smoothly despite some conversation about THAAD, according to Yonhap.
Beijing has asked the deployment be canceled because of THAAD's powerful radar and regional surveillance capabilities.