Ex-Hatter Cook becomes a Mariner
The 28-year-old had been released by the Hatters at the end of the season where he made just 16 appearances, scoring one goal.
Cook had been limited to one start in the league, that coming at Grimsby, where he was sent off after just 33 minutes for picking up to bookings.
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Hide AdHe didn't feature again for Luton from there, leaving the club when his contract expired having netted five times in 58 games.
Cook, who had played in the Premier League for his boyhood club Sunderland prior to joining Luton in June 2016, became Mariners boss Michael Jolley's fifth new addition of the summer.
On moving to Blundell Park, said: "I'm over the moon to get it finally done. I've been speaking for a good few weeks to the manager, so I'm just glad to get all the paperwork signed and can't wait to get started."