Spurs confirmed the signing of the Danish midfielder on Tuesday, paying Southampton a reported £15-million fee.
The arrival of the former Bayern Munich player could push club-record signing Tanguy Ndombele closer to the exit. The Frenchman, who appeared to be at odds with Mourinho during his first season with the team, has been linked with a potential switch to Inter Milan.
Hojbjerg, who made 33 Premier League appearances while playing at the base of Southampton's midfield this past season, should add a steady presence in the center of the pitch for Spurs.
Capped 33 times for Denmark to date, he made 128 total appearances during his four-year spell at St. Mary's Stadium.