Delaney had been offered a new deal by Wanderers who were also promoted from League Two but was unable to agree terms.
He made 23 appearances for Bolton last season but lost his place in January after a red card against Tranmere.
The former Republic of Ireland Under-21 international said:"I’m excited to get started and have a new challenge for this coming season.
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"The gaffer spoke to me about two weeks ago and since he rang me, then I wanted to get it done as soon as possible.
"I’ll always give 100%, I’ll put my body on the line and I want to do my best to keep as many clean sheets next season and hopefully produce a couple of goals at the other end."
Delaney is Morecambe's fourth signing of the summer, with the squad set to have a much different look to the one which won promotion via the League Two play-offs.
Shrimps manager Stephen Robinson said: "We’re delighted to have him on board, I think he’ll excel here.
"He’s a big, strong player, he’s good on the ball and he had some good games for Bolton last year.
"He can play in the middle of a back three, he can play in the left of a back three or in a back four.
"I believe there’s another level in him as well, he’s still learning the game."
Delaney started his career with Irish side Wexford Youth before joining Burton Albion.
After a loan spell back in Ireland at Cork City, he signed for Rochdale and made 57 appearances for the Spotland outfit.
He gained further League One experience on loan at AFC Wimbledon and then joined Bolton in January 2020.
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