A slightly-revised planning application by the new leaseholders is due to go before Stratford District Council later this month and, if approved, work could start later this year.
The Byron group was founded in 2007 and now has more than 50 restaurants — 37 in London — as it continues to grow across the UK.
Tom Byng, Byron’s founder, said: “Bell Court is a perfect fit for Byron.
“We are confident that local people and visitors to this lovely, historic town will appreciate our obsession with doing things properly and our commitment to raising expectations around customer service.”
UK and European Investments bought the lease last year for the shopping centre.
John Stacey, asset management director, said: “We are very confident of attracting other well-known names.”
Claire’s Accessories closed down suddenly last week. No one from the store’s head office could be contacted for comment this week.