Eastham was released by the Seasiders at the end of last season, during which he enjoyed a second lengthy loan spell with Dale's fierce local rivals Bury.
The 22-year-old told his new club's official website: "I want to flourish into the player I believe I can be and I am definitely in the right place to do that.
"I had a couple of offers from some sides in the league above and a couple in this division but Keith and Chris laid out their intentions for Rochdale Football Club and showed a big desire for me to sign.
"In the early days at Blackpool the manager Ian Holloway really liked me and I had a couple of games in the first team and was told I did well in those games.
"However, I needed to play regularly and the gaffer said honestly I wasn't ready at that time so I was loaned out to gain experience.
"I have had four loan spells, twice at Cheltenham and twice at Bury and I believe those experiences have moulded me into the player I am now."