The 21-year-old defender said his heart was set on coming to Ibrox as soon as he heard Steven Gerrard was interested in bringing him into his squad.
Edmundson was a key player for Oldham last season making over 50 appearances and was named in the League Two team of the year.
Speaking exclusively to RangersTV he said: “It’s a dream come true. It is finally over the line so I’m happy and I can’t wait to get going. Obviously I’m only a young player but to come to Rangers is a massive opportunity and I feel like I can live up to the expectation.
“There were a few clubs interested but as soon as I heard Rangers were interested in me there was only one place I wanted to come.
“I don’t really think it sunk in at first but after a few days and when I met Steven Gerrard it was unbelievable and I can’t wait to play under him. He has done everything there is to do in football so when he wants you to play for him you can’t turn that opportunity down.
Edmundson is also looking forward to getting the opportunity to play and train alongside experienced international players such as Jermain Defoe, Allan McGregor and Steven Davis.
He added: “They have done everything there is to do in football so I will be asking them questions and trying to learn off of them to become a better player.
“It is going to be massive for me getting to train alongside Jermain Defoe, I will be learning off him in training trying to learn what strikers do and don’t like and become and better player.”
The defender is excited about the opportunity of playing in front of 50,000 fans at Ibrox.
“Like I said before it is a dream come true to pull on the Rangers shirt,” he said. “It is unbelievable and I just can’t wait to get going.
Last season Edmundson played almost every league game for Oldham, missing only the last game through injury.
He said: “I felt like last year at Oldham was the season I needed to break through and I felt like I done that. I’ve had good coaching when I was in the youth team, they’ve helped me a lot and I’ve had experienced professionals with me in the first team and it’s helped me along the way.
“I’m only young and I’ve got a lot to learn but I feel at the minute I am comfy on the ball, good in the air and a solid defender so hopefully I can show everyone what I am about.
Edmundson is preparing to travel to Portugal with the squad this weekend for a week of pre-season training.
He added: “It will be good, I haven’t met the lads yet so getting to fly out to Portugal I’ll be in with them straight away. I have got my initiation song ready for them so hopefully I can impress and it will be nice to meet them all.”