Buchanan, who has committed himself until 2028, cost Inter a reported 10 million euros ($10.9 million).
Buchanan, 24, began his professional career with New England Revolution in the MLS before joining Club Brugge in January 2022.
He made 67 appearances in all competitions for the Belgian club, including six last season in the Champions League.
Last year he was a member of the Canada side that featured in the World Cup in Qatar. He has made 35 international appearances, scoring four goals.
Inter have 45 points heading into matchday 19 this weekend, two more than Juventus.
Simone Inzaghi's side face Verona on Saturday without their Canadian recruit, who is expected to make his debut the following weekend at Monza.
