Ray Kelvin told the Press Association that a combination of hedging against currency fluctuations and a dollar-denominated income from its US operations will help the firm keep prices from rising.
He said: "We were hedged for two years and we have one year left on that. We're a public company, we don't gamble with things like this, plus we also have a big dollar income.
"So there won't be any price increases this year, we'll remain great value."
The fall in the value of the pound since Britain's decision to quit the European Union has meant several retailers have had to ramp up prices as weaker sterling makes imports more expensive.
But Ted Baker's US operations, which include retail and wholesale, will help cushion any currency blow, Mr Kelvin added.
His comments come as Ted Baker announced a 17.9% increase in retail sales for the eight weeks to January 7.
But the company flagged a "backdrop of ongoing external factors", which Mr Kelvin defined as the rise of the internet and political uncertainty.
On Brexit he said that, while Ted Baker has not seen any impact on the British consumer yet, "what will be will be - we will be prepared".