Bignot, who joins from Solihull Moors, succeeds Paul Hurst at Blundell Park following the latter's move to League One side Shrewsbury Town.
The 42-year-old takes over a Grimsby side sitting eighth in League Two, just one point off the playoff places after 15 games.
"Firstly, I would like to place on record my gratitude to the then-chairman of Solihull Moors Nigel Collins and present incumbent Trevor Stevens for both giving me my first managerial opportunity. I'd also like to extend that gratitude to the board and Mike Turl for allowing me to take a football team and go on to build a football club - I'm very proud of not only on the pitch but off it also," he told the club's official website.
"The six years I have spent at Solihull Moors have moulded me into the person I am today and I can honestly say The Moors will always have a genuine place in my heart. But now, looking to the future, I am delighted to be at Grimsby Town and I am excited by the project. This is not just a job.
"We've got a great squad of players and I am looking forward to getting to know and understand them. Today is an important day in terms of meeting the staff and players and putting my plans in place for the week."
Bignot's first match in charge of the Mariners will come against Sheffield United in the Checkatrade Trophy on Wednesday night before they host Barnet in League Two on Saturday.