"Ed is really excited for fatherhood. He helped pick out a stroller for the baby," the insider said, adding the child is due to be born "any day now."
Whether the pair expect a son or daughter was not reported.
Norton, 43, is known for his movies "Moonrise Kingdom," "The Incredible Hulk," "American History X" and "Primal Fear."
Robertson is a Canadian film producer.
The couple got engaged in 2011 after six years of dating, UsMagazine.com said.