Robertson led Scotland for defeat to Belgium last week.
But Kompany said: "Most of us in football have come from humble backgrounds. Whatever way you get there, it is just great to see him doing well.
"Andy is now playing to such a high level with Liverpool and now he is captain of his country. He has come a long way in a short space of time.
"I do think he is a great example. If you look at every single club, you will find a lot of young lads coming through who probably used to be ball boys or something.
"If you have work rate and desire and ability like him, it is not so much of a surprise. It is natural progress.
"I knew of him when he was playing in Scotland even before he joined Hull City.
"I play Football Manager, so I was well aware of him. I actually signed him back then because good left-backs are hard to come by. I took a gamble on him, but it paid off."