Howard failed to produce his best form for Pools following his return to Victoria Park in the summer of 2012 and, after joining Sheffield Wednesday on loan for the final month of last season, his future was the subject of plenty of speculation.
But the 37-year-old striker has opted for another campaign at Hartlepool under new boss Cooper, installed as John Hughes' permanent successor in May.
"He had a few options to explore over the summer, but Steve has now pinned his colours firmly to the mast," Cooper told the club's official website ahead of Saturday's opening clash at Rochdale.
"I think he's come back in to training and enjoyed what's been happening, now he's fired up and determined to put behind him what happened last season.
"If he does decide to retire at the end of next season then I think he wants to make sure that he goes out on a high by producing the goods for this club.
"He wants to repay the fans and although he knows that won't be easy, it's something he's determined to do - and the way he can do it is to get in the best possible shape he can be and get out there and score goals."