The 44-year-old, who scored the first goal in the Premier League for Sheffield United against Manchester United in 1992, joins the club from the University of Leeds where he had been director of football.
"Deane said he is grateful to have this opportunity in Sarpsborg 08 and is looking forward to taking on the job," the club said in a statement on Wednesday, adding that the new manager would address a news conference on Thursday.
"He is very keen to preserve the values of the club."
Despite stints in Portugal and Australia, the well-travelled striker is best known from his time at Leeds United and Sheffield United in his native Yorkshire.
He was capped three times during his brief international career.
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