Mourinho's Chelsea side will take on Van Gaal's Manchester United team in the Premier League at Old Trafford on Sunday.
Robben was brought to Chelsea by Mourinho in his first spell at Stamford Bridge before playing under Van Gaal at Bayern Munich and later with the Netherlands national side.
Van Gaal and Mourinho - who worked together while the Dutchman was in charge at Barcelona - will lock horns at Old Trafford on Sunday and Robben believes there are parallels to be drawn between the experienced duo.
"They are both very demanding, really intense and what they ask from their players is the same kind of intensity," the Bayern winger told The Telegraph.
"They are the same in the way they prepare things, the way they live and breathe football and tactics every second of the day almost.
"When I came to Chelsea and worked with Mourinho, it was my first time abroad, so that was an important stage for me.
"But I have also worked under Van Gaal, and now [Pep] Guardiola and I feel so privileged to have worked for these great coaches because it has certainly helped me make good steps in my career."
Robben enjoyed a hugely successful time at Chelsea under Mourinho - winning two Premier League titles and an FA Cup before making the move to Real Madrid.
After two years at Real, where he won just one league title during a disappointing spell, Van Gaal helped him rediscover form at Bayern to the point where he is now one of the finest players in the world.
The 30-year-old revealed there were certain differences between the two as well, with Mourinho placing more of an emphasis on collective efforts.
"Mourinho was always very strong for his players and you needed to deliver for him.focus on collective strength," he added.
"For me, it was good. It was also very special because, in my first year, we won the league, Chelsea's first in 50 years, and that was important for everybody at the club. But for me the big thing I learnt from Mourinho was about mentality.
"He taught us to be strong, collectively, and also strong for yourself.
"Van Gaal is the kind of guy who can really make individual players better. It was the most important step of my career to go from Real Madrid to Bayern. It was the best move of my career, coming here and working under him.
"It really gave me a lot of confidence and a new way of working."
