Wilson, 51, a former player and manager at city rivals Sheffield Wednesday, was unveiled as the Blades' fourth boss in nine months amid chants of "We hate Wilson" and "You don't know what you're doing" by a protest group of around 150-strong, who had gathered in the club car park.
Wilson said: "I'm not foolish enough to think it's going to be anything other then very difficult to come across the divide, but as far as I'm concerned it's a massive privilege to come to a club of this size with its tradition and the support of Kevin and the directors."
He added: "It's not going to be easy. We have to play a certain brand of football and win games to win the fans over - but you have to do that anywhere.
"It will be difficult. We understand that, but every manager is in a difficult position. We always are and always will be, while some [jobs] are more difficult than others.
"But I promise you we'll work very, very hard for this football club. I'm very determined and I think eventually we'll win people over."
Wilson, born in Wigan, made 24 appearances for Northern Ireland as a player and counts Brighton, Luton, Sheffield Wednesday and Barnsley among his former clubs.
He was installed as Barnsley's player-manager in 1994 and guided the Tykes to the top flight three years later for the first time in the club's history.
He also won promotion with Hartlepool, but MK Dons were relegated while he was in charge and he left Swindon deep in the mire when he quit as boss there in March this year.
Wilson has also been sacked as Bristol City manager and was unable to halt Sheffield Wednesday's slide towards the Premier League trapdoor before suffering the same fate at Hillsborough in 2000.
Source: PA
Source: PA