He's now back in Chicago, but his heart never left the Windy City.
"Guys always joked in the dressing room about cutting the cord, but it was obviously tough," he told the Chicago Tribune's Jimmy Greenfield. "Five successful years in Chicago. It was a team that took a chance on me in the draft and gave me an opportunity my first year in pro, then winning two Stanley Cups.
"Becoming friends with all those guys in the locker room, it was really tough to let go. I never really did. I had to move on, but (Chicago) was a part of me. I was never going to forget it and move on completely."
Shaw, a restricted free agent at the time, was traded to Montreal in 2016 for a pair of second-round picks - one of which was used to select Alex DeBrincat. Three days later, Shaw signed a six-year deal with the Canadiens carrying a $3.9-million cap hit, a price too steep for the Blackhawks.
The 27-year-old says he enjoyed his time playing for the Canadiens' storied franchise, but Shaw was excited upon learning he was being traded back to the Blackhawks on June 30.
"It's something you wish for," he said. "You don't actually think it's going to come true. It did and I'm excited, I'm happy. (I'm) a lot different from when I left three years ago. I have a wife, a kid and I've matured a little bit. Chicago's still going to get the same hockey player but maybe a little bit of a different person."
Shaw has been regarded as one of the NHL's best pests during his seven-year career, but he's also taken strides offensively. Last season with the Canadiens, he tallied a career-high 47 points while only playing 63 games.