According to the statement, the Championship outfit have reached an agreement with the Belgium club, with the player having been offered a three-year deal.
The transfer fee that Burnley will have to pay for the services of the 26-year-old striker has not been announced, though.
The statement on Burnley's official website also added that Vossen has yet to agree personal terms and pass a medical.
Blow for Celtic?
This will come as a disappointment for Scottish Championship club Celtic, who were reportedly interested in Vossen.
The Scottish Sun recently claimed that Championship duo Middlesbrough and Sheffield Wednesday and Belgian outfit Club Brugge were interested in Vossen.
Good signing for Burnley?
Vossen played on loan for Middlesbrough last season. The 26-year-old scored eight goals and created 26 chances in 36 league appearances for Boro, helping them reach the Championship playoff final.
The Belgian, who was often deployed in a deep-lying role, had a pass accuracy of 71% and a shot accuracy of 55%, and he won 37 headers, eight dribbles and 18 tackles.