Blackman, 23, arrives at Bramall Lane after the Blades’ number one keeper Simon Moore sustained a knee injury during the friendly at Rotherham last week.
“Jamal has been our number one target right the way through the summer,” United manager Chris Wilder told the Sky Bet Championship club’s official website.
“There was a situation with his new contract at Chelsea so we’ve had to be patient but we are delighted that he is with us now because there were a few clubs in for him. He provides genuine competition in an important area of the pitch.”
Blackman, who has been capped by England at various youth levels, spent last season on loan with Wycombe and has also had temporary spells with Middlesbrough and Swedish club Ostersunds FK.