The Castleford-born 29-year-old former York City man has penned a two-year deal with the option of an additional 12 months.
Woolford played under Adkins at Scunthorpe United and his most recent club was Millwall.
Adkins said: “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’s arrival follows the extension of Diego De Girolamo’s stay at the Lane with the signing of a new contract extension.