The former England international, who has been an ever-present in the Premier League this season, reached the milestone in Sunday's 2-1 home victory over Liverpool.
And Portuguese manager Mourinho lauded the 33-year-old's achievements, particularly in the current campaign.
"I think more important than the 600 matches is the fact he played every minute in the 19 matches in the Premier League this season," he said.
"Only Petr Cech has done that and he is a goalkeeper.
"John is the only outfield player that played 19 times, 90 minutes, which is amazing for a player that last season lots of people were thinking is going down (hill).
"He is showing fantastic quality, I'm happy for him, as I told him at the beginning of the season the players I had in the past I have a special connection with them. But I don't give positions because I like or I have a relationship with them.
"At this moment every game he is getting is not because he is my man, my friend or I respect him from my first period. He's getting these minutes because he is playing fantastically well."
Victory over Liverpool left Chelsea third in the English top flight at the halfway stage, with a trip to Southampton up next for the Stamford Bridge outfit.
