The 33-year-old is predominantly a left-back, but can play anywhere across the back line.
United boss Neil Warnock was delighted to complete the deal, telling the club's official website: "I've been looking to see if I can get one or two leaders in. Paul is a player who I have had my eye on for a couple of weeks - since I came in - but for whatever reason we just couldn't quite get it over the line.
"Now we've been able to do that I'm delighted. This is a great club for him and it gives us a chance to have a look at him with a view to next season."
The experienced defender has made over 500 career appearances since starting out as a trainee with Watford. He made almost 250 of those appearances for West Brom before joining Premier League Bolton in a £1m deal in January 2010 after impressing on loan.
He was a regular in the Bolton side up until the turn of the year. He has made 76 appearances for the Trotters and featured 20 times this season.