The company aims to open a Â£50m site at Temple Works in Holbeck by 2019 creating 200 jobs to produce trench coats.
Two existing centres in Castleford and Keighley will close under the plans, with 770 staff expected to relocate.
Councillors have agreed to allocate land for the move and provide a grant to landscape part of the site.
Under the plans, the Grade I listed Temple Works building will be restored with work on the site in South Bank, Holbeck due to begin next year.
Senior councillors have been asked to allow city officials to form legal agreements with Burberry for the "disposal of council assets on Bath Road, Sweet Street and Leodis Court".
A grant of up to Â£750,000 will be provided to create a "new public space" at the front of Temple Works.
A report is to be prepared by June 2016 detailing the final negotiations and legal agreements with Burberry.
Earlier this month councillor Judith Blake, leader of Leeds City Council, said: "We welcome this significant investment in Leeds and are proud that Yorkshire will continue to be the manufacturing home of this great British business, bringing jobs, training and regeneration to the area."
Plans by global fashion brand Burberry to open a weaving centre in Leeds have been backed by the city council.