Chelsea manager Mourinho worked under Robson at Sporting Lisbon, Porto and Barcelona in the 1990s and the 72-year-old said: "He's had a remarkable first season in English football.
"It's incredible. At the beginning of the season Arsenal and Manchester United were in pole position and looking strong and Chelsea had to get ahead of them.
"I didn't think they could at the beginning of the season but he's come in and modelled the side. He's done fantastically.
"I take great pride in the fact that he's done well. I'm really proud of him."
Under Mourinho Chelsea have already won the League Cup and the league title and take on Liverpool on the second leg of a Champions League semi-final on Tuesday.
Robson, who lost his job as Newcastle manager at the start of the season, said 42-year-old Mourinho's managerial qualities had been evident at an early stage.
"We worked together for six years at Porto and Sporting Lisbon and then I invited him to Barcelona to be my interpreter.
"We worked on the pitch every day. He is very bright, very alert, he's a student of the game.
"He's learnt well and he's done great at Chelsea. He inherited a good squad and then brought in a contingent of other players which has added to and strengthened the squad.
"He's handled the big players very, very well. He's a young lad, he's not a father figure like I am or Sir Alex (Ferguson) or Arsene (Wenger) or (Bill) Shankly or Bill Nicholson.
"The cream on the cake would be if they clinch the Champions League, that would be incredible."
