He takes over from Richard Coggin, who left the independent digital agency in December last year.
This will be Montgomery's first role in a digital agency. He will be responsible for Grand Union's creative output across its entire roster of clients, including Energy Savings Trust, Abbey and Boots.
Rob Forshaw, a partner and founder of Grand Union, said: "We looked at a number of different places, but soon realised we couldn't find the person we were looking for from a digital agency. I've known and admired Giles' work long before I started Grand Union, and I believe he's one of the best copywriters in the world."
Montgomery said: "I love the internet, but you have to remember it's just another medium. You're still left with the same questions: what's the big idea and how do you best communicate that?"