The 31-year-old striker made his debut in last night's 4-0 hammering of East Fife in the Scottish Communities League Cup first round.
And, having pulled on the light blue jersey, Kyle is desperate to make his mark for Ally McCoist's side – despite his move sparking domestic unrest.
"My brothers and I all grew up football-mad, but they support both sides of the Old Firm," he explained.
"When I was a kid I was just crazy about football and would have watched anyone at any time without having a real feel for one or the other.
"But my brother who is a Celtic fan texted me as soon as he heard that I had signed for Rangers to tell me that he had lost a brother! Well, we don't speak that often anyway.
"The minute I knew that Rangers wanted me I was on my way. A chance like this does not come every day."
After a torrid time out of the game with a hip injury, Kyle believes he is back to his best and ready to be part of the Rangers revival.
A decade ago Alex McLeish tried to sign the player when he was an up-and-coming talent at Sunderland, only for Peter Reid to quash the move.
But, as Kyle has explained, the minute he got back into Scottish football with his deal at Rugby Park, he had a feeling he could end up at Ibrox.
"It's strange how it has all come about and you could never have imagined this," he said. "But when I was at Kilmarnock I knew if I played well there would always be the chance of something coming off.
"I've obviously had a nightmare time when I was out of the game for a year-and-a-half with injury, but I am fresh, I'm hungry and the minute I heard from Ally [McCoist] about coming here, there was no hesitation on my part.
"At the beginning of my career big Alex tried to sign me, but at that time Sunderland were having none of it.
"Whatever has happened it is one of the biggest clubs in the world and it is a privilege to get this opportunity."
Peterhead on Saturday might seem an unlikely destination for the beginning of what may be a significant journey, but Kyle wants only to be a part it.
"This is a chance for all of us to write our names into a significant chapter in the history of this club," he said. "I want to be part of that. This is Rangers, whatever has happened, and I know what that means to so many people.
"It is important we approach all these games in the right frame of mind. We have the chance to do something special and be a part of a team that gets Rangers back on to the stage they deserve to be on.
"I feel good and I am convinced I can play a big part in making that happen. I've been out of the game for so long that I need a little fitness work, but I'm in the best shape of my career."