54-year-old Whiteside is currently a non-executive director of the bakery firm and will start in the company's top job on 4 February.
The position was created when, in December, the current Greggs chief executive Ken McMeikan announced his intention to leave the business and take the helm at food supplier Brakes.
Following a handover period, McMeikan, who played a key role in the row which followed the Government's decision to introduce the so-called Pasty Tax, will leave on 8 March.
Meanwhile, the now vacant post at Punch Taverns will not be filled immediately - the Burton-upon-Trent-based pubco has made current non-executive chairman Stephen Billingham the executive chairman.
Neil Griffiths, currently the property and turnaround director at Punch, will become a chief operating officer for the business.
Possible restructuring
“I would like to thank Roger for his significant contribution to the group over the last 4 years," said Billingham.
The businessman took up his role as chairman in 2011, at the same time as Whiteside became chief executive, when the demerger from managed division, Spirit, was completed.
"Roger and the board have set out a clear operational plan to return the core estate to growth and maximise value from our non-core assets.
I am confident that with the appointment of Neil Griffiths as chief operating officer and with the experienced management team in place at Punch we will continue with the progress we are making in delivering on these key strategic goals," he added.
Punch Taverns is currently embarking on a significant disposal programme with the aim of creating a profitable core estate of just 3,000 pubs - it currently owns around 4,500.
Last October, Whiteside revealed the company had begun initial discussions with shareholders and stakeholders about a possible restructuring of the business.
Derek Netherton, chairman of Greggs said the company was 'delighted' to announce Whiteside's appointment.
"Not only has he got considerable management experience in retailing and food but also, as a non-executive director of Greggs during a period of significant change, he has been involved in developing the strategy.
He is very well respected within the company and his appointment will enable a smooth transition in what is still a challenging consumer environment."