Wilcox has been rewarded for the League Two club's fine form since he took caretaker charge following the departure of Brian Laws last month.
A spell which has produced 13 points from five games has lifted Scunthorpe to third in the table as they seek promotion back to the third tier of English football.
Chairman Peter Swann is "delighted" to have agreed a permanent deal with Wilcox, who made over 100 appearances for the club as a player between 1997 and 2003, saying he "could not see beyond" handing him the reins.
"It has become quite obvious over the five games in charge that Russ has taken this opportunity with both hands, not only bringing the players together, but being rewarded for that with five great results," Swann added.
"It would be prudent for us to have a period of time before the January transfer window to sit down and chat about players and that is better done with him as permanent manager.
"Russ will continue to be assisted by Tony Daws and the other coaches until a time when he wishes to appoint a permanent number two."
Wilcox's first game in permanent charge of Scunthorpe sees them travel to second-bottom Bury on Thursday.
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