Clarets manager Vincent Kompany has played a decisive role in convincing the Swiss youngster to move to Turf Moor amid competition from several European clubs.
Burnley will pay €18 million to secure the Swiss forward’s services.
Amdouni caught the eye with his performances in the recent U21 European Championship, preceded by a stellar 2022/23 season at Basel, where he bagged 22 goals and seven assists in all competitions.
The 22-year-old was also the top scorer of the Europa Conference League with seven goals, helping Basel reach the semi-finals.
A highly versatile player who can play from attack to midfield, Amdouni is tipped for big things in the future.
The Swiss youngster is the latest piece of transfer business by Burnley in what is turning out to be a busy summer transfer window.
Kompany, who led Burnley to the Championship title last season, is making full use of the transfer window to ensure his squad is ready for the Premier League.
Dara O’Shea and Lawrence Vigoroux have completed their moves to Turf Moor, while Jordan Beyer’s loan deal has also been converted to a permanent transfer.
More signings could follow, with Manchester City goalkeeper James Trafford one step away from joining the Clarets and free agent Nathan Redmond linked with a move to the club.