Scully is Shrewsbury’s seventh signing ahead of the new League Two season following the arrivals of goalkeeper Elyh Harrison, defenders Tom Anderson, Sam Stubbs and Will Boyle along with Tom Sang and midfielder Sam Clucas.
Director of football Micky Moore said Scully would bring “something different” to Appleton’s squad.
“Michael and Anthony go back many years and they had a very successful time working together before,” Moore said.
“I’m really happy we got this over the line before the season starts because we believe he offers something different to what we’ve got in the squad.
“He’s someone we’ve targeted for a while and I know Michael and Anthony have been in touch for a few weeks already.
“We’re thrilled to have him and we’re excited to see what he does over the coming season.”