Joseph Colley, director of communications for the commission, said: "The President will make a television statement conceding the election within the next three hours."
"Our commissioner was called and informed and we are confident the president will concede," he added.
Earlier, the head of the commission Alieu Momar Njie, told reporters in Gambia, "It's really unique that someone who has been ruling this country for so long has accepted defeat."
Barrow, a property developer, won more than 45% of the vote with 263,515 ballots cast for him.
He reportedly previously worked as a security guard at the Argos retail store in London where he once tackled a shoplifter, according to reports in UK newspapers.
Speaking to CNN by phone from the Gambian capital Banjul, Barrow said: "We are very, very, very happy. The people have been very patient."
Asked what he planned to do with the incumbent president's human rights violations, he said: "We will follow the rule of law...he has led a good campaign and conceded. But everything will be done according to the law."
President Jammeh seized power in 1994 in a military coup and has been in power ever since. Human rights groups have described his regime as abusive, with hundreds of political prisoners languishing in jail.
On the eve of the election, websites and phone lines were blocked and remained so as polls opened on Thursday.
Throughout election day, heavy paramilitary presence was reported at poll stations as Gambians cast their votes using the country's unique marbles and drums system.
In April, the UDP's national organizing secretary was beaten to death while in custody of security services, according to a Human Rights Watch report.
Sabrina Mahtani of Amnesty International said in response to news that Jammeh had conceded defeat: "For many years, the people of Gambia have suffered numerous abuses, including horrific human rights violations and oppression."
"The last two weeks have shown how much Gambians of all parties value free speech," she said. "There is a huge obligation now for the future administration to transform the human rights situation in Gambia, freeing political prisoners, removing repressive laws and entrenching newly found freedoms."
Jammeh also attracted heavy criticism for claiming that he had created a herbal remedy for AIDS. He also once threatened to behead gay people.
The small West African nation is the fourth largest source of migrants arriving in Italy
, despite having a population of less than two million people.