The 49-year-old had confirmed on Thursday that talks with owner Massimo Cellino were at an advanced stage and the agreement was confirmed at lunch time before the match with Cardiff City
The former academy coach becomes the club's third boss of the season, replacing Slovenian Darko Milanic.
Redfearn, who won 10 points from four games in caretaker charge earlier this season could't stop his side losing 3-1 to a ressurgent Cardiff City side under their new boss Russel Slade.
Leeds started the season under former Forest Green boss Dave Hockaday but he was sacked after just six games.
Redfearn was instilled as caretaker manager and recorded three wins and one draw in four games before Milanic was appointed as head coach in September.
The former Sturm Graz boss failed to win any of his six games in charge and was sacked last Saturday after the 2-1 defeat by Wolves.
Redfearn revealed on Thursday that he had sought assurances from Cellino that he would be retained by the club if the Italian chose to replace him as head coach.
"You can't guarantee anything in football and if results aren't right then things have got to change," he told BBC Radio Leeds.
"I'll still be part of the picture and the bigger plan and I want to be part of that.
"I'm prepared to sacrifice myself to the club because I can see the bigger picture getting better here."
Cellino joked before the nmatch that redfearn could be in charge for five years - lol to that given his track record!