Speaking to RangersTV, Aasgaard outlined that new head coach Russell Martin played a considerable role in his decision to move north of the border, having played against his sides in England.
"I'm delighted to be here," said the 23-year-old. "It's been quite a few days waiting for it but I'm really happy to get it over the line.
"When I heard [about Rangers' interest], I was over the moon. I've played against the manager a few times and I've always seen myself in his team.
"It was quite an easy decision to be fair. I love the amount of games here, the stature of the club and that itself is enough.
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"I think just having the trust from the manager is really important and just being here one day, I can already see he wants me to express myself in his system and I'm really looking forward to play a part.
"I remember when we played his Swansea teams, we never really touched the ball!
"I always thought it'd be fun to play in that sort of team."
Asgaard joins Rangers from Luton, a club he only signed for at the beginning of this year.
He did spend time in Liverpool's academy before moving to Wigan, where he made 163 appearances.
"I played for Liverpool for five years," he said. "I was a young kid, 14, moved to Wigan, and kind of developed through the academy there and made my debut when I was 18.
"It was four or five years of progression, really. It kind of started off quite raw, playing a lot of games, but just finding my feet.
"And then coming into the age of 19, 20, I really started to impose myself on our team. We won the league and won it well and got promoted, and it was a chance to show myself in the championship.
"I think I did quite well, although we got relegated. But last season and the season before was really where I started to step into my own body and really become the player I am.
"I grew a lot of confidence and scored some goals."
A full Norway international, Aasgaard made his debut for his country in March, scoring and bagging an assist in a 5-0 win over Moldova.
"They really took me in well," he said. "To be fair, I feel really part of the group. We've got a top, top group. We've had a strong start to the World Cup qualifiers.
"So, yeah, to play in the World Cup next year is a big goal for me.
"Hopefully, I can show the manager that I'm ready with some performances here.
"I feel at home already. The facilities are fantastic. It's a really good change in me. I can't wait.
"It just feels like the right thing in my career. To be playing in front of some amazing fans at an amazing stadium, it's what I've been dreaming of.
"I'd say I have a bit of flair, I'm full of confidence and not afraid to shoot from distance.
"I like to link up with my teammates and form connections at the top of the pitch.
"I like to be part of the build-up phase as well as getting in the box and getting my goals."