The highly rated England Under-21 international will spend the 2018/19 campaign with the Blades, who finished 10th in their first season back in the second tier last term.
Henderson sees his long-term future with the Reds, having signed a new contract with the club last week that will run until at least June 2020, with the option for a further year.
However, such is the fierce competition for places in the goalkeeping department at all levels at United, he makes the move to Bramall Lane in search of more regular first-team football on the back of a successful loan spell at Shrewsbury Town in 2017/18.