"Looking back, there were all these small moments—certainly moments where I was like, 'Wow, this could really be something,'" Laura Warshauer tells PEOPLE

Kate Middleton and Prince William's connection was obvious to those around them right from the start.

The royal couple, who met as college freshmen in 2001 at the University of St. Andrews in Scotland, "definitely had chemistry," Laura Warshauer, a New Jersey native and St. Andrews student who lived in the same dorm as the pair, says in PEOPLE's new special edition William & Kate: 10 Joyous Years.

"Whenever Kate was in the room, Will was obviously paying attention to her," Warshauer continues. "When we'd be sitting at lunch in the dining hall and the two of them would be talking, it was amazing to see how natural it was, how they had so much to say to each other. Looking back, there were all these small moments—certainly moments where I was like, 'Wow, this could really be something.'"

It was. By their sophomore year, the pair had become housemates, sharing a four-bedroom flat with two other friends and frequently walking to classes together.

Prince William - Catherine, Duchess of Cambridge
Kate Middleton and Prince William
| Credit: Kensington Palace/Instagram

In their 2010 engagement interview, the couple, who recently celebrated their 10th wedding anniversary, opened up about their college romance.

"I actually think I went bright red when I met you and sort of scuttled off, feeling very shy about meeting you," Kate said about William. "It did take a bit of time for us to get to know each other but we did become very close friends from quite early."

William added, "We moved in together as friends. We lived with a couple of others as well, and it just sort of blossomed from there, really. We just saw more of each other, and you know, hung out a bit more and did stuff."

PEOPLE's new special edition William & Kate: 10 Joyous Years is available now at Amazon and wherever magazines are sold.

Cover of People's William & Kate Anniversary Issue

That natural ease they have with one another is even more evident today, as fans could see in their first YouTube video, which saw the parents of three giggling and playfully teasing one another.

"By the way, be careful what you say now because these guys, they're filming everything," William quipped while pointing to the camera.

"I know!" Kate responded with a laugh.

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In another playful moment, Kate corrects her husband's pronunciation as he attempts the Irish language. "You don't need to roll your r's," she said.

"Do I not roll those?" William replied, to which Kate shakes her head and says, "No."