Ms Emin was said to be upset by Ecclesbourne's plans to sell the blanket because it could not afford the pound;1,000 to pound;3,000 framing costs.
She threatened to take the blanket away from the school.
Sotheby's thought it was likely the blanket, which Emin made with 60 Year 4 children at the Islington school in 2000, would fetch pound;35,000.
On Wednesday, however, the school said it had reached a compromise with Ms Emin and Jay Jopling's White Cube, the gallery which represents her.
Nigel Williams, the chair of governors at Ecclesbourne, said: "The White Cube and Ms Emin have agreed to pay for the hanging costs and the frame.
"The contract we are going to draw up says the work is the school's as long as we do not try to sell it."
Originally, Ecclesbourne had hoped that the money raised from auctioning the eight-feet by four-feet blanket would pay for art equipment and other artists-in-residence.
Mr Williams added: "I am pleased with the outcome because we did not want to lose the blanket as a piece of social history of the school. The problem was that we couldn't afford the pound;3,000 to frame it."
Mr Williams, a minister at nearby Canonbury Community Baptist Church, said he hoped that the blanket, which would probably be hung in the school dining hall, would also be displayed in his church.
Rachael Earnshaw, head of Soho parish school, was given a quilt by Tracey Emin for a fund-raising auction organised by the PTA. The auction, which raised pound;150,000, also included works donated by Damien Hirst and Gavin Turk.
Ms Earnshaw said: "Tracey Emin was extremely generous. She donated a fabric embroidery piece specifically for that purpose. We were very grateful to her."
She said the school had artists-in-residence, but always made sure they drew up contracts so that the use and destination of the work was agreed.