Edmondson still had another year on his contract at Leeds but Simpson has saluted the Whites for the way in which his club were able to land the forward on a free transfer, especially with the striker having "better offers" elsewhere.
The Whites still hold a sell-on clause as part of the deal and Simpson says he would have no qualms with Edmondson using Carlisle as a launchpad to achieve bigger and better things.
Edmondson has already stepped out under former England youth boss Simpson for the Three Lions under-19s and the Cumbrians chief is full of praise for both Leeds and his new striker.
"He had a year left at Leeds and when we enquired about him I actually thought it would be too big of an ask," said Simpson to Carlisle United's official website.
"But I could only ask. The minute I spoke to his agent then eventually spoke to Ryan, and they were absolutely up for it.
"I know he had better offers to go elsewhere, but the fortunate thing is that he knows me from working with me before.
"He wanted to come here because he thinks this is where he can come and develop.
“He knows he’s got a manager who knows him and understands him. I’m really looking forward to working with him, he’s got a good personality and he’s really keen to learn and develop.
“If it’s a case of him using us to kick on his career, I don’t mind that, because I want somebody who has got that fire in his belly.
“He needs to come in and do the job, to wear that number 9 shirt and deal with what comes with that.
“The challenge is for him to show me and the rest of the staff that he deserves to start as our striker.
"He’s competing with some other lads who think they should be in the team, which is only a good thing.
“He’s had some loan moves and things like that, but I do think he’s at a stage where he knows he needs to show people what he’s about and put a bit of a marker down.
“It’s been frustrating that we’ve had to wait, it’s been agreed for three or four weeks, but he’s been on holiday over in Australia.
“He only arrived back on Tuesday then he was straight in for his medical and to sign everything."
Harrogate-born ex-York City forward Edmondson joined Leeds as a 16-year-old back in November 2017.
The striker then made his Whites first team debut in that season's Championship finale at home to QPR as a 74th-minute substitute under former boss Paul Heckingbottom in May 2017.
Edmondson's second of just two first team outings for Leeds then arrived the following season under new Whites head coach Marcelo Bielsa who brought him in on in the 71st minute of September's 2-1 defeat at home to Birmingham City.
But the forward then suffered a knee injury which required surgery the following Spring and the biggest feature of his time at Leeds since has been four separate loan spells at Aberdeen, Northampton Town, Fleetwood Town and Port Vale.
Six-foot-two Edmondson has always been highly thought of at Leeds and Simpson added: "I think Ryan is a really good signing for us. He’s a player I know, he was involved in my England U19s, so I know of him and I’ve watched a lot of him.
“He’s had a bit of an up and down time with his loan moves, some have worked and some haven’t. He was unfortunate up at Aberdeen that he got injured.
“I wanted a big target man, he’s a bit of a throwback, but I wanted an old-school number 9. He absolutely works his socks off, he can get goals and get on the end of things.
“He can hold it up and create, and he’s a bloody pest for centre backs."