George Calombaris, a MasterChef Australia judge, said the money would be repaid at "the highest priority".
His company, MAdE Establishment, said 162 current employees at its Melbourne eateries had already been repaid, and former employees were being contacted.
On average each staff member was owed more than A$16,000, the group said.
"I am sorry we have messed up and let you down on a fundamental issue, which is to ensure our people are paid their full entitlements," Mr Calombaris said in a statement to staff.
"I am devastated by what has happened and we have been working extremely hard to fix this."
The company said the errors, dating back to 2011, were caused by miscalculating overtime pay rates.
Mr Calombaris said the group was first alerted to the issue in 2015 by Australia's Fair Work Ombudsman.
"Regrettably, our attention to detail at that time wasn't at a level it should have been," he said.
The underpayments affected staff at high-profile restaurants The Press Club, Gazi and Hellenic Republic.
Former staff have been encouraged to contact the company.
An Australian celebrity chef has apologised after his restaurant group underpaid staff A$2.6m (£1.6m; $2m).