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Current News International CIO Andrew Hickey is leaving the company later in the year to "develop a portfolio of consultancy work" and Cheesbrough will start in the autumn.
Cheesbrough said, "I have had a terrific few years at The Telegraph. Leaving was a difficult decision for me to make, but News International is fantastically positioned to take advantage of the next stage of growth in the digital marketplace and I am looking forward to joining the group at this exciting time."
He will report to chief executive Rebekah Brooks, who said, "I am delighted to welcome someone of Paul's calibre to the team. He has exceptional experience in leading technology teams for content businesses and he joins us at a defining moment for our digital strategy. His work with editorial and commercial groups will be enormously relevant to our plans to invest and to innovate for our customers."
The Times and the Sunday Times have recently launched pay walls for their news websites, and the rest of the publishing industry is watching closely to see if the initiative will be a success.
Cheesbrough will be responsible for all of News International's technology platforms, and developing and providing the digital infrastructure.
Before joining the Telegraph in 2007, he was controller of digital media at the BBC.