Curle couldn't stand in Adams' way after winger expressed his desire to move back up north
Curle and Adams have a close relationship but after discussing the situation earlier this month, a move back up north was deemed best for all parties.
"Nicky played a big part in our promotion last season and he will always be remembered fondly for his two spells with the club," said Curle.
"Everyone knows the relationship that Nicky has with the club and also my own relationship with him having signed him twice, but after having various conversations with Nicky this transfer window, this move makes a lot of sense for him for a number of reasons.
“Having the security of an 18-month contract was obviously important plus the location worked well with his young family, but also Nicky, with his personality, wants to be playing 90 minutes week in, week out and Oldham know they have a player who will produce for them.
"Nicky is a first-class professional who has served this club extremely well and he leaves with our very best wishes."
In total, Adams played 107 games and scored six goals across his two spells at the Cobblers.