The England Under-21 international joined Boro earlier this month until the end of the season after spending the first half of the season also in the Championship with Nottingham Forest.
Middlesbrough's new manager Aitor Karanka was previously Mourinho's assistant at Real Madrid and Chalobah feels that the Spaniard will help his development.
"I got back from Forest, met with Jose and he told me I was coming here. I was really happy with it as I'm suited to the style," Chalobah told BBC Tees.
The 19-year-old made his Boro debut from the bench in the 2-0 defeat at Leicester City on Saturday.