Robertson was signed by Bruce at Hull City in 2014 and has since gone on to establish himself as one of the best fullbacks in world football.
The 25-year-old believes Bruce contributed to his rise and thinks the Englishman will do well at St. James' Park.
"There has been a lot of negativity around it and I think that is really unfair for a man who has achieved what he has," the Scotsman winner told the Telegraph. "I hope he gets the backing he deserves.
"I did not think I was ready after only a year in full-time football with Dundee and felt it would be better to wait, but I spoke to Steve for 15 or 20 minutes and he convinced me I was good enough for that level.
"For the two-and-a-half years I was with him he was a different class and helped make me the player I am today. So personally, I am delighted for him. Newcastle is a huge club and I hope he does well – not against us, obviously – but in every other game."