Roebuck, who previously worked as the multichannel marketing director at French Connection, will be tasked with developing a customer and digital strategy across the business and exploring new digital partnerships.
The British company has suffered a string of setbacks in the last year, including profit warnings, an inventory overstatement, a decision to suspend dividend payments and several management changes after misconduct allegations against founder and top shareholder Ray Kelvin - which he has denied.
Lindsay Page's promotion to chief executive officer last April was seen as a turning point for the company, which has been trying to move past all the bad publicity.
Page, however, left after only eight months, along with Chairman David Bernstein.
"The composition of the board will be something for the new chair to review, once appointed," the company said on Wednesday.
Last week, Ted Baker said the value of stock on its balance sheet was overstated by 58 million pounds ($76.24 million) as at Jan. 26, 2019, more than double its preliminary estimate of up to 25 million pounds.
Pressure has been mounting for management as the company also battles weak consumer demand. Last month, it issued a third profit warning for the year and said its performance during November and the Black Friday sales period, in contrast to some other retailers, was below expectations.
(Reporting by Tanishaa Nadkar in Bengaluru; Editing by Bernard Orr)