The League One outfit chief, Martin Thomas, also said he would 'love' to see the now-retired boxer to fight Anthony Joshua at their 6,500-seater Mazuma Stadium!
Fury's 'Gypsy King' brand will feature on the club's home and away playing shorts for the 2022/23 season.
And Thomas revealed how the deal came about, as well as hinting at a future partnership with the Manchester-born fighter.
"Tyson actually owns a building right at the side of the ground so we see him on a daily basis," he told talkSPORT.
"Whenever he's in Morecambe, he's in and around the club so we speak to him and see him on a daily basis."
"We were having a chat one day and we just got talking about how things were going for the club and he said he'd like to help out where he could.
"So we've done this one to start with, which is the playing shorts. and we'll have another exciting one to come, which is a bit further."
After beating Dillian Whyte in April, Fury announced he was retiring but has been persistently linked with a return to the ring.
He recently claimed he would fight Joshua for free as long as the clash would be shown on free-to-air TV and all tickets cost nothing.
And, hoping Fury would continue his generoisty towards his local club, Thomas joked that it would 'not be a problem' for them to host what would be a British boxing classic at the third-tier stadium.
When asked about Fury vs Joshua potentially happening at the Shrimps' ground, Thomas added: "I'd love for that to happen!
"Yeah, AJ and Tyson here, we'll pack him in, not a problem at all."