The 28-year-old has been training with the Reds for the past week and today penned a short-term contract at Oakwell.
Born in Airdrie, Woods started as a trainee with Leeds before moving to Sunderland and then South Yorkshire with Rotherham in 2006.
After a season with the Millers, Woods moved to Doncaster Rovers and went on to make over 100 appearances for the Keepmoat club.