Compton became Cooper's first signing of the summer on Thursday, linking up with Pools' new boss for a second time after previously working under him at Bradford.
"I am really excited," Compton told Hartlepool's official website, "I was with Colin at Bradford City and I got on really well with him. As soon as I had the phone call, I jumped at the chance to work with him again.
"He brings out the best in me and hopefully we can spark together again and have a good season.
"Other clubs came in and offered me stuff but one of the main reasons I am here is because of Colin and hopefully I can repay the faith he has shown in me.
"You can have a laugh and a joke with him but he is strict and fair so you know where you are with him.
"He tells you what to do and if you don't do it, you are not playing and if you do it then you'll be doing well.
"I am glad he's got his opportunity, I think he is a fantastic coach and all the lads at Bradford appreciated his coaching abilities so I am just looking forward to getting started."
Compton joins Hartlepool following his release from Colchester, where he spent the second half of last season after leaving Portsmouth.