Beckford will remain with the club until the end of the season when he will be able to walk away on a free transfer due to his contract having run out.
Beckford told the club website: "I want to finish what I have been striving to do for the last two seasons. I want to help promote Leeds out of a division they don't belong in."
He added: "Every time I put on the Leeds United shirt I give 100% and can assure the fans, the manager and everyone connected with the club that I will continue to do that."
Beckford, who will be available to leave on a free transfer in the summer, handed in a transfer request days before the Old Trafford win and had been linked to Newcastle.
Simon Grayson added: "I'm keen to draw a line under the situation and now we can all move on together."