Rainford, 31, finished as the joint-second top scorer in the league last season, with 22 goals, having spent the early part of the campaign with Clitheroe and Widnes.
He hit the ground running upon joining the Rams, scoring seven goals in his first six matches, and helped them reach the play-offs, ironically at the expense of Linnets.
Linnets boss Michael Ellison said: "Jamie's goalscoring record speaks for itself and it's clear what he's going to bring to the side apart from his goals - he brings with him a wealth of experience, a winning mentality and it's an understatement to say I'm delighted to have him on board."
Well-travelled Rainford counts Colwyn Bay, Glossop North End, Prescot Cables, Marine, Chester, Halifax Town and AFC Fylde amongst his former clubs.
Meanwhile, Runcorn have also signed young centre-back Louis Coyne from Prescot Cables.
Coyne, 21, started last season at Marine, alongside Linnets defender Peter Wylie, before being granted a release to return to Cables, where he went on to make 20 appearances.
Ellison added: "Louis is a great signing for us he has the attributes that I look for in a centre half.
"He a big lad, good in the air and he can play as well.
"He had a number of clubs chasing his signature. I'm delighted he chose Runcorn and I'm looking forward to working with him."