Henderson has agreed a season-long loan with the Blades.
“I can't wait to go there to build on the last season I had at Shrewsbury," said Henderson.
“It's in the division above and showing that progression by going on to the next bigger stage, in front of 30,000 passionate fans at Bramall Lane. I can't wait to go there and perform and connect with them. I'm sure it will be a successful season.
“Sheffield United are a massive club and it's a massive city for football. They've got that rivalry with Sheffield Wednesday and I'm looking forward to those games coming up as well. I can't wait to get there and push up the division."