The U.S. embassy in Kabul had denied visas for the girls earlier this month for unknown reasons.
However, VOA's White House bureau chief, Steve Herman, reported Wednesday that Trump granted the girls what is known as a parole - reversing the earlier decision to bar them from the U.S. - that will allow them to come to Washington for 20 days.
A student team from Gambia also was granted visas last week after initially being rejected.
The president of FIRST Global, which organized the robotics competition, is former Democratic congressman and retired U.S. Navy Admiral Joe Sestak. He thanked the White House and the State Department for clearing obstacles to the Afghan and Gambian students' travel to the United States. Teams from all 157 countries that have entered the competition now will be taking part, he added.
The three-day robotics competition begins Sunday in Washington.
FIRST Global Challenge holds the yearly contest to build up interest in science, technology, engineering and math across the world.
The group says the focus of the competition is finding solutions to problems in such fields as water, energy, medicine and food production.