Two previous attempts to secure visas, which involved traveling 500 miles to the U.S. Embassy in Kabul, had failed.
On Tuesday, U.S congressmen Joe Courtney and Suzanne Bonamici sent a letter signed by 53 members of the United States House of Representatives to the U.S Secretary of State Rex Tillerson urging him to issue U.S visas for the girls. Afghanistan isn't one of the six countries targeted by President Trump's travel ban.
When news began to spread of their visa denial, a number of groups openly criticised the U.S. government, with similar events around the world offering to host the girls at their competitions.
The Taliban, ousted by the US -led coalition in 2001, denied schooling to girls when they ruled the war-torn country.
The all-girls robotics team from Afghanistan has arrived in Washington, D.C.
The journey has been a long one. Ultimately the State Department, which adjudicates visa applications, asked the Homeland Security Department to let them in on "parole", a temporary status used only in exceptional circumstances to let in someone who is otherwise ineligible to enter the country.
The young women are in the USA for the inaugural FIRST Global Challenge, in which teams of young women and men from around the world showcase robots they created.
The team's robot can sort balls, recognize blue and orange, and move objects to their proper places, according to the AP. The girls are hoping to receive the documentation there that they need to travel to the United States.
President Donald Trump reportedly intervened and urged USA officials to let the girls into the country for the competition.
"Seventeen years ago, this would not have been possible at all", Mohib said in an interview. But Mohib said that based on discussions with US officials, it appears the girls were rebuffed due to concerns they would not return to Afghanistan.
Mehraban says: "It's a happy moment for our team". "We are going from a war-torn country and the goal is to show the capability of Afghan women".
The worldwide competition, which runs July 16 to 18, is staged annually by the nonprofit First Global. Teams from all 157 countries that have entered the competition now will be taking part, he added.
Earlier, visas issued to the students of Gambia. "I honestly believe the greatest power of America is the power to convene, to bring together nations and see their differences are so much less than what they have in common".
Before Trump stepped in to help, the competition's organizers had arranged for a group of Afghan-American students living in the U.S.to operate the Afghan team's robot, which is already in the country, while the Middle Eastern teenagers watched via Skype.
With the final obstacles to their journey removed, the girls can now turn their focus back to robotics.
"Afghanistan is a war-torn country where it is hard for women to improve", said 15-year-old Lida Azizi. "But now this is a big chance for us to attend in the competitions and also it's good for our country".