Speed, 40, who has signed a three-year contract, has retained the services of Blackwell's assistant Sam Ellis and hopes to appoint a new coach in time for his first game in charge at Middlesbrough on Sunday.
Blackwell, 51, departed the npower Championship club by mutual consent on Saturday after the 3-0 home defeat to former Blades manager Neil Warnock's QPR. That followed United's Carling Cup exit at Hartlepool four days earlier.
Speed, appointed player-coach by Blackwell in July 2009, said: "I'm delighted to be given the opportunity to manage a great club like Sheffield United.
"These opportunities don't come around very often and I feel this is my time and that I'm ready for the step-up.
"I would have liked it to have been in better circumstances. We were all disappointed on Saturday and I'd like to thank Kevin Blackwell for everything he did for me personally.
"He helped me in many aspects of coaching and management and I'm sure it won't be too long before he's back in the game.
"He did a lot of work here behind the scenes that will stand this club in good stead in the future."
Source: PA
Source: PA