United have installed a buy-back clause in the deal for the 22-year-old Belgian, Spanish media reported.
Januzaj has agreed a five-year contract with the Basque side and will be presented officially on Thursday after attending his first training session.
"Thank you to some of the coaches and staff that work at Manchester United to make it a great club," Januzaj said on Instagram.
"Unfortunately, my time at the club has come to an end and it didn't go the way I wanted it to go, but I will always have love for Manchester United."
Januzaj broke into the United team in 2013 under manager David Moyes and scored twice in his first start in a Premier League game against Sunderland.
But he never built on that early success and netted only five goals in 66 appearances for United before being sent on-loan to Borussia Dortmund and Sunderland.
($1 = 0.8760 euros)
($1 = 0.7762 pounds)
(Reporting by Rik Sharma, editing by Ed Osmond)
Share
