Manager Gary Johnson had offered the former Leicester City man a new deal with Town but had warned McKay that he was unlikely to be a first choice in the upcoming campaign.
"I wish him every success," Johnson told the official club website, saying that the player had been unlucky to sustain an injury just as the new manager arrived at the club.
McKay made 53 league starts and 21 substitute appearances for the Cobblers, scoring 13 goals.
***Updated***Inverness Caledonian Thistle have agreed terms with the player who will now be plying his trade in the SPL next season while fellow striker Tadhg Purcell is set for a loan spell with former club Darlington as he continues his recovery from injury.
"Tadhg is at a stage now where it would be good for him. Darlington could give him an opportunity," Johnson told BBC Look East.
"He'd be going there to get some games and we'd assess it from there."