King is free to sign outside of the transfer window as he left Birmingham City before the deadline earlier this month.
He is a proven goalscorer in the Football League, having impressed at the likes of Watford, Coventry City and Birmingham.
United - tipped to be among the League One frontrunners this season - have taken just four points from their opening seven fixtures, netting only five goals.
After spending time training with the Blades, King has now been handed a deal by manager David Weir.
Weir said: "We have struggled for goals and he fits the criteria. He's a goalscorer, he has experience and he has been there and done it.
"He played in the last round of internationals for Jamaica so he is fit. As a team we have not scored enough goals and he can help us."
King told United's official website: "Goals win games; I bring goals but also experience to try and get the boys rallied and help the cause.
"It's a great set-up, a great fanbase and, if selected, I can bring something to the table."