Naysmith, 28, has signed a three-year deal at Bramall Lane - ending a six-and-half-year stay with the Toffees.
It is the second piece of business between the sides in as many days, after the Blades agreed to sell Phil Jagielka to David Moyes' side for £4million.
Naysmith told the club's website: "Coming to play under Bryan Robson makes me really excited and, after speaking with the chairman, I am keen and happy to be here.
"I was always there or thereabouts at Everton but they had several established players and if you were out injured it was difficult to force your way back in."
Naysmith also revealed the new management team of Bryan Robson and Brian Kidd at Bramall Lane was a big reason behind his decision to swap the Premier League for the Championship.
"I spoke to (Everton captain) Phil Neville about working with Brian Kidd and he had nothing but praise for his training methods and he was sure I would enjoy it immensely.
"Both Robson and Kidd are born winners.
"This is a big club who have done very well in recent years and were unlucky in the Premiership last season.
"I have no problems with dropping a division, as I feel we will only be here (in the second tier) for one year. We have a great squad with plenty of experience so we should be aiming to get promoted at the first attempt."
Like Jagielka, Naysmith is a versatile player and would be happy to inherit the England B international's role as jack-of-all trades for United.
He said: "I will play anywhere, although I see myself as a left-back.
"I can play in midfield, though, and did on occasions for Everton last season."