The 29-year-old, released by Millwall, worked under manager Adkins at Scunthorpe, helping the Iron to promotion.
Woolford has the option of a third year with the Blades, and Adkins is delighted to complete his first signing.
He told the club’s official website: “We signed Martyn at Scunthorpe and he scored the winning goal at Wembley to win us promotion from League One.
“We are very aware of the talents Martyn brings to Bramall Lane. He can play in several attacking positions, is fit, strong, robust, honest, hard-working and has a fantastic professional attitude.
“He has been consistently available for selection over many seasons and knows the demands required of this level.”
Woolford added: “Being a Yorkshireman I know how big this club is and I’m looking forward to getting started with the lads. It is great to be working with Nigel Adkins once again and everyone knows what the major goal is.”