The developer submitted a revised application in February for 173,000 sq ft of retail anchored by a 50,000 sq ft Primark and 20,000 sq ft Next.
Redevelopment of the former Pioneer car park at Curzon Street replaces a previous scheme known as the Oval development, which stalled after Debenhams pulled out of talks to anchor the centre.
Burnley Council chief executive Steve Rumbelow welcomed the planning approval and said it was a “big step forward” for the town.
“The plans set out a clear vision for the transformation of that part of the town centre,” he added.
“Burnley faces stiff competition from other towns and cities and we have to offer shoppers as wide a range of shops as possible in order to bring them to Burnley to spend their money.”
A spokesman for Henry Boot said: “This is testament to the ongoing hard work and strong partnership between Henry Boot and Burnley Council which is set to deliver positive results during these testing economic times.”