The 35-year-old midfielder put pen to paper after returning from holiday.
Woods was a regular starter in Jamie Hamill’s side last season after returning to the club for a second spell last summer, having been at Stair Park from 2017 to 2018 before a three-year stint with East Kilbride.
Woods, who netted five times in 40 appearances last season, said: “When the gaffer spoke to me at the end of the season, it was agreed.
“Looking back over the season, we had good spells and it is good to get a bit of continuity. I was not going to leave or change teams again.”
Stranraer will kick off their Premier Sports Cup group at home to Queen’s Park on Saturday, July 9.
Their fixture schedule sees them away to Hamilton on Tuesday, July 12, at home to Dundee on Saturday, July 16, and away to Forfar on Tuesday, July 19.