The Blades have beaten off interest form Bristol City to land the Salford-born forward, who was given the green light to move away from Villa Park earlier this week.
Hogan becomes United’s third capture of the transfer window following the earlier additions of Gary Madine and Kieran Dowell.
On his signing, Blades chief Chris Wilder said: “I have made no secret of my admiration for Scott and his abilities, we made enquiries about him in the last window and we have had to be patient.
“He is a player we know a lot about and we are confident that he will be a great addition to what we already have. Options at the top end of the pitch are vitally important and in the situation we find ourselves in, Scott offers us a new dimension.
“Also, Scott had options but he made it clear that he wanted to join us and that goes a long way in my book.”