The Ostersundsposten newspaper said the club had accepted a bid of about 20 million Swedish crowns ($2.89 million) for the Gambian-born 21-year-old who has scored 10 goals this season.
"The club is both glad and proud and wishes Modou all the best," club chairman Daniel Kindberg told the newspaper, adding that Barrow will play his final game for promotion-chasing Ostersund on Tuesday before leaving for Swansea the next day.
Although he declined to comment on the transfer fee, Kindberg said: "I've never been involved in a bigger deal, and I don't know if I'll ever be involved in anything similar again."
Barrow, who had a spell on trial at Bolton Wanderers, joins a Swansea side that got off to a flying start in the new Premier League season with a 2-1 win at Manchester United last weekend.
($1 = 6.9168 Swedish Crowns)
- Sports & Recreation