Cummins, 35, joined the club in December 2018 and scored the famous 120th minute winner that took Marine to the FA Cup third round in 2020/21.
He scored 44 goals in 102 appearances.
Manager Neil Young said: “Niall has been a great captain and ambassador for our football club over the years he has been here.
“He took a fairly big gamble dropping down when he first came in on loan and scored lots of goals until his terrible injury curtailed his season and ours.
“True to his word on his recovery from injury he stuck with the club and the fans and the rest shall we say is there for all to see ‘literally’.
“We all wish him and his family well with what comes next and thank him for his considerable contribution to our recent successes.
“I’m also sorry to see James leave but he informed me that he has received an offer from another club that he felt he couldn’t turn down.”
Marine return to the NPL Premier Division for the 2022/23 season having beaten Runcorn Linnets in the NPL West Division play-off final last month.