I'm not disputing Gwan's suggestion, but I don't think it's a very postive thing to say.
I don't believe in anyone being someone's replacement, because you are an individual in your own right. Being a replacement reminds me of being like a robot, you can replace a car, or a computer but not a person. A person is unique and not in place of someone else. You wouldn't get a divorce and get a replacement wife/husband so why be a replacement employee?
I would suggest,
"I took the position left vacant by Julie," or (more naturally to me) "I took the vacancy (position) after Julie left.