Woods is the club's second new marking of the mid year planning for the League One campaign.
The 32-year-old brings an abundance of experience to Prenton Park having started his vocation at Liverpool in 2006.
His first club far from Anfield was Dunfermline where he gone through five years and picked up advancement to the Scottish Premier League.
In 2011, Woods moved to then League One side, Huddersfield Town.
He added another advancement to his name with the Yorkshire side, helping them achieve the Championship in the wake of beating Sheffield United on penalties at Wembley.
Woods made the switch over the Pennines to Preston North End where he would appreciate an promotion winning first season at Deepdale.
He showed up in the Championship for Preston before moving to Bradford in 2019.
Having finalised the deal, Woods said: I'm delighted to get it over the line and I can't wait to get going now.
As soon as I heard Tranmere were interested, it was the only place I wanted to be. I've played in this league before and earned a couple of promotions.
I know I?m coming into a team with back-to-back promotions so hopefully we can push on.
I can play on the right or the left of the defence and I like to attack when we?ve got the ball.
I can't wait to get going.
Manager Micky Mellon was delighted to bring Woods into the squad for next season.
I'm really happy to bring Calum into the group, he?s experienced at this level, he's a local lad and he?s still really hungry to do well.
It's important that when we get the opportunity, in a very competitive market, that we get value for who we're bringing in.
Calum can play a number of positions and we?re delighted to be working with him next season.