His deputy, Tony Gallagher, takes over as Daily Telegraph editor, while Benedict Brogan, assistant editor and chief political commentator, will become deputy editor.
Lewis, the paper's youngest ever editor, recently completed a three-month management training course at Harvard University.
The new role will him set up and run an 'entrepreneurial unit' which will have a staff of 50 and be based in Euston, away from the company's main office in Victoria.
As managing director, digital, he will also oversee Telegraph Media Group's existing digital businesses.
Under the new arrangements, Gallagher and The Sunday Telegraph editor Ian MacGregor will continue to report to Lewis. Brogan is appointed deputy editor of The Daily Telegraph. Mark Skipworth remains executive editor, overseeing the Saturday edition while Chris Evans, executive head of news, becomes Gallagher's number three.
Lewis will remain also as editor in chief of the Telegraph titles and website and he will continue to report to the chief executive, Murdoch MacLennan.
MacLennan said: 'I am delighted that Will has taken up this vital challenge. For the last three years, he has done a first class job editing The Daily Telegraph whilst successfully integrating our print and digital editorial operations. Will also orchestrated undoubtedly the biggest story of the decade, our highlighting of the systematic abuse of MPs’ expenses.
'I believe now is the time to fast forward to the next stage of our digital transformation. Using the Telegraph’s powerful brand and reputation, Will has been charged with building a digital unit designed to capitalise on cutting edge ideas, driving new revenue streams by better serving our customers.'
Lewis said: 'I am very excited by this new opportunity. As Editor-in-Chief I will continue to supervise the strategy and overall content of our newspapers and website, whilst working on our digital revenue streams.
'It is a tribute to our chairman, Aidan Barclay, and the Barclay family that they have invested millions of pounds in this exciting venture, which will help us rapidly expand our digital operations.'