Gaffney, who previously played under Darrell Clarke at Bristol Rovers, was confirmed as a Saddlers player shortly after today’s League Two clash with Grimsby.
The 29-year-old, who is originally from Galway in Ireland, scored 11 times in 47 appearances for Salford last season.
“I’m absolutely delighted to join the club for the season,” Gaffney said.
“It happened pretty quickly over the last few days but when I got the chance to join, I was more than happy to do so.
“I spoke to the manager on Friday and I know all about him and about the staff that are here as well, like Marcus and Brian, so he didn’t really have to say that much to convince me to come here.
“I know some of the lads who are here as well, like James Clarke and Stuart Sinclair, so I was really happy to take the opportunity to come here.
“It’s the first time in my career that I am re-signing for a manager so I know exactly what is expected of me, I know all about the training and what is expected of us as players.
“Having played with James and Sinco, I know straight away what they are like as players so it’s easier to come into a group that I know a few faces in.”