The 20-year-old midfielder signed a four-year deal from Sheffield Wednesday this summer and began training with his new team-mates at Lennoxtown when they returned for pre-season earlier this month.
Shaw could make his debut for the Hoops against his former club when new boss Ange Postecoglou's side take on Sheffield Wednesday behind closed doors in Wales next Wednesday.
However, he is looking ahead to the time when he will see and hear supporters in the stands when he runs out at Celtic Park.
He told the club's official website. "I'm looking forward to playing in front of the Celtic fans.
"That's what I'm looking forward to most. I've heard all about the atmosphere at Celtic Park and hopefully I'll score a goal and hear that crowd. Playing in that atmosphere will be something I'll remember forever.
"Walking out and hearing the roar of the crowd will give you a massive adrenaline boost.
"It gives you so much more energy, maybe nervous energy, but good nervous energy."
Shaw has been impressed by the friendliness and facilities at Lennoxtown.
He said: "It's been good so far. I've been here for a few weeks and I'm enjoying training. I feel settled in where I'm living now so it's been good.
"I've been talking to Scott Robertson and Luca Connell a lot. I've known Luca from playing back in England.
"Everyone's been sound, to be honest. Those two have been really good with me and made me feel very welcome.
"Lennoxtown is really good. There are a lot of quality pitches and everything's been spot-on.
"I'm quite blown away by how nice it all is. Inside there's a lot of great equipment to use so we have everything we could possibly need to help us.
"The training's been tough, especially the first week with all the running. It's good, though. That's all in the tank now.
"You get your fitness up and get sharper. I've enjoyed the tempo of it and the standard's been really high in training so I'm feeling ready to go."