Cobbold joined De La Rue in January 2011 as a replacement for James Hussey, who resigned after taking responsibility for the production problems uncovered at the firm's Overton mill in 2010.
He leaves to take up the same role at UBM, the international media and events business, where he will replace David Levin. De La Rue said it would appoint head hunters to start the search for a replacement and to work with the Board's Nomination Committee to identify suitable internal and external candidates.
De La Rue's non-executive chairman Philip Rogerson has been appointed executive chairman on an interim basis, while group finance director Colin Child has returned to the chief operating officer role he last held following Hussey's departure in 2010.
Once a successor is found and appointed, both Rogerson and Child will return to their former roles.
Rogerson told PrintWeek that he would be stepping up his involvement from today but that Child would be responsible for moving the business along "day to day".
Cobbold's departure comes in the middle of the tender for the £1bn Bank of England print contract, which De La Rue has held since 2003, the result of which will be announced in the Autumn ahead of the April 2015 start date.
Rogerson admitted that the timing of Cobbold's departure was "not ideal" in terms of the BoE tender, but added: "Tim was not involved on a day to day basis in the Bank of England tender - we have a really good team of very talented individuals who will continue to work on the tender and the key decisions as we go forward will be taken by the board as was always intended."
Rogerson confirmed that the Bank of England tender was the single biggest commercial issue for De La Rue but stressed that this would not influence the company's search for a successor in terms of imposing a deadline on the process.
"If we did end up with an external candidate then presumably they would have a notice period, which would make it unlikely that they would be appointed [before September]," he said. "I don't think that's a problem - the important thing is to get the best man for the job."
While Cobbold only tendered his resignation last night, De La Rue agreed it was in both parties' best interests to waive the six month notice period in his contract. "We all agreed that a sensible break point would be the end of the financial year," said Rogerson.
During Cobbold's three-year tenure he implemented an Improvement Plan that raised the firm's operating profit from £40m in 2011 to an anticipated £90m in the current financial year - albeit falling short of the stated £100m target.
Cobbold said: "I am very proud of what the De La Rue team has achieved over the past three years. The business is much stronger today with a significantly improved financial performance, and is well placed for the future."
De La Rue's share price was largely unmoved by the news, falling less than 1% to 814.5p at the time of writing.
