The 22-year-old forward moved to the Liberty Stadium from Swedish side Ostersunds in the close-season on a short-term deal.
Barrow has impressed for Swansea's Under-21 side with five goals in seven appearances and he made his first-team breakthrough by coming off the bench in November's 2-1 Premier League victory against Arsenal.
Further league cameos have followed in matches against Manchester City and Crystal Palace, while Barrow scored his first senior Swansea goal in last Saturday's 6-2 victory at Tranmere Rovers in the FA Cup.
After signing his new deal, Barrow spoke of his delight at extending his stay in South Wales.
"It's great to sign the new contract," Barrow told Swansea's official website. "It was an easy decision.
"I came here until January initially, but now I can settle for the next four years.
"My girlfriend and I really like it here and we are really happy. I was delighted to sign the contract.
"It's been amazing to play for the first team since joining in the summer. I have tried to work as hard as possible in training and when I've been given my chance, but I know I must keep working for further opportunities."
