The Pilgrims have snapped up the 33-year-old former Millwall, Sheffield United and Grimsby Town man, who has also appeared for the likes of York City, Scunthorpe United and Bristol City.
Woolford has arrived at The Jakemans Stadium following a short spell with Hyde United in the BetVictor Northern Premier Division and is eligible to make his Pilgrims' debut against Darlington on Saturday.
He did not feature for the Tigers in their solitary Emirates FA Cup appearance earlier in the campaign and is therefore free to play for the Pilgrims in the competition.
Reflecting on Woolford's arrival, United manager Craig Elliott told bufc.co.uk: "Martyn is versatile and left-footed and he played nearly 40 games in League 2 last season.
"He has played nearly 400 games in the Football League, for some big clubs, so he will give us vital experience that we are perhaps lacking at times.
"He's hungry to do well and he's a fit lad so I am sure he will be a big asset for us."
PIC: Lee Blease (Grimsby Town).