The 23-year-old arrives at Bloomfield Road having been involved with the first-team at City in the Carabao Cup and spent last season on loan at Lommel SK in Belgium.
Grimshaw spoke of his excitement of joining the new Sky Bet Championship side, he told Blackpool’s website: “I’m happy and really excited to be here. I’ve worked really hard in my career to get to this point.
“I want to progress further here at Blackpool. I’m looking forward to working under Neil Critchley and Steve Banks and alongside the goalkeepers that are already here.”
Blackpool earlier announced the signing of left-back Reece James on an initial three-year deal with the option of a further 12 months.
James will join newly-promoted Sky Bet Championship side upon the expiry of his contract at Doncaster on July 1.
The 27-year-old becomes Neil Critchley’s first signing of the summer ahead of the 2021-22 campaign.
Speaking to Blackpool’s official website, James said: “As I knew there was a bit of interest, it was something that I really wanted to follow up and jump at.
“Playing in the Championship was something that I’d set out to do following what had happened in the season, so it was a massive pull to come here.”