The 31-year-old arrived at the Tigers last summer and has scored seven goals in 15 appearances so far in 2022/23.
Redshaw has played for a wealth of clubs throughout his career, including time at both Ashton United and Chester last season.
He follows in the footsteps of his father Ray, who had a spell with the Tigers in the 1982/83 campaign.
“I’m delighted to extend my stay,” he said. “I’ve had a positive start here and I’m really enjoying my football.
“It was a no-brainer really. As soon as the offer came about, I wanted to get it done.
“It’s a great set of lads, and I’m playing for a manager who knows how to get the best out of me.
“It ticked all the boxes really, and I’m delighted to be here.”
The club have also announced that goalkeeper Dan Atherton will remain at the club until the end of the season.
The former Warrington Town shot-stopper was brought in to replace Gio Bellagambi, who was recently recalled by parent club Huddersfield Town.
Atherton made his debut in their FA Cup defeat to Buxton earlier this month.
Photo credit: Sean Walsh
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