Heywood, 30, adds cover for the injured Paul Jones, has league experience with Brentford and Swindon and was released by Grimsby in February.
The duo become the third and fourth new arrivals of the summer after Danny Forrest and Ciaran Donnelly.
Fellow wideman Simon Wiles has also signed a new deal with the club after impressing during a short-term stint last season.
Meanwhile the Bluebirds continue their search for a new goalkeeper after a proposed new arrival stalled on a move to Holker Street.
Saturday's 2-0 defeat by Manchester City's elite squad handed former Morecambe goalkeeper Steven Drench another 90 minutes in Bluebirds colours.
However joint-bosses Dave Bayliss and Darren Sheridan are yet to tie up a permanent replacement for the departed Stuart Tomlinson and Tim Deasy.
Source: BBC Sport
Source: BBC Sport