Kelly, 32, joins the club from Bala Town and has previously featured for the likes of Chester City, Burton Albion, South Melbourne and Port Melbourne Sharks.
Corrigan made 11 appearances during his maiden season with the Purps before the curtailed season.
The experienced full-back has a long working relationship with manager Michael Ellison and his backroom team, having had a successful period together at Runcorn Linnets.
Ellison said: “Shaun is a great signing for us. He brings with him a wealth of experience and after meeting with him it was clear he would fit into what we’re trying to do.
“Shaun had a number of clubs chasing him and I’m delighted he has chosen the Purps.
“Corrigan is a top lad on and off the pitch, he’s got a wealth of experience and a wand of a left foot."
Keep up-to-date with our exclusive email newsletters.
Subscribe