Tigers manager Nigel Adkins has been running the rule over the free agent, formerly on the books of the likes of Aston Villa,West Brom and Birmingham City, after inviting him to train with the club after recently leaving MLS side Portland Timbers.
Ridgewell will provide valuable defensive cover with Hull's back-four options currently stretched, with Ondrej Mazuch, Reece Burke and Jordy De Wijs being fitness doubts for the weekend clash with Stoke City.
The 34-year-old spent five years in the United States and made 115 appearances for the club, helping them win the MLS Cup in 2015.
“I’m delighted to sign having spent the last few days up here training with the boys,” said Ridgewell.
“It’s nice to be back in English football and back in the Championship.
"The boys have really welcomed me and this is a team looking to move in the right direction.
"They’ve been on a good run up until last weekend, and it’s a group that is prepared to work hard for each other and hopefully I can use my experience to help the side to push on a little bit more.”