The £1.5million striker sealed his switch from Preston on Saturday after admitting it was too good a move to turn down.
Garner revealed he has had one eye on the Light Blues since his days as a teenager at Blackburn, when he shared a dressing room with Italian defender Amoruso.
Garner - who has signed a three-year deal after being lured north by Mark Warburton - told RangersTV: “You’ve seen some massive stars up here, and when I was a kid at Blackburn, Lorenzo Amoruso came down from Rangers and didn’t shut up about what it was like when he was here.
“So I have memories of that, and now I’m just really looking forward to getting involved and playing my part here.
“It was a couple of weeks ago now I first heard about the interest from Rangers and once I spoke to the manager here and heard his ideas, I knew there was only one place I wanted to go and I really wanted to be a part of things here.
“I spoke to a few other clubs, but I was happy with where I was at the time, but once Rangers came in I felt it was an opportunity I couldn’t turn down. The possibility of winning trophies and medals, as well as playing in front of massive crowds every week, really made me want to be a part of things.”
Meanwhile, midfielder Matt Crooks will step up his recovery from an ankle injury when he runs out for Gers’ Under-20 side against St Mirren on Tuesday night.
The summer signing from Accrington Stanley has not kicked a ball since March but has now returned to full training.
However, the 22-year-old admits it has taken him a while to get back up to speed.
“It felt weird to put my boots back on, they were a bit tight,” said Crooks. “It was a nice experience to get back out there.
“The first two days I trained I was terrible but I am enjoying it now and it is just nice to be back playing football.
“I am back training properly so it’s all positive, it took me a couple of days to get going and find my touch again but I feel like I am getting there.
“I was half expecting a pain or to not feel as comfortable but as soon as I got into it I was fine.
“It’s not been a great time, I’ve not really trained at all and coming to a new club you just want to get started and get straight into it and make a good impression.
“It has been tougher than I expected but you just have to get on with it because there is nothing you can do about it; you just have to be positive, come in and do your best and see where it takes you.
“I was pretty depressed after about five days into the trip to America, I felt like I was wasting my time and wasting the team’s time not actually being able to do anything.
“This is the longest I have ever been out and I’m not really used to being injured - the first few days after I came back I was thinking ‘what is going on? I have lost it completely’ and I was panicking a bit.
“It is something new to me so in a way it has been a good experience and I have learnt from it, I’m still young so in that sense I’ve gained something from it I guess.”