Darbyshire was formerly the paper's executive editor and Lewis an assistant editor responsible for business coverage, a role he will retain.
It is only weeks since Lewis joined from The Sunday Times, where he was business editor for three years following more than eight years at the Financial Times.
Daily Telegraph editor Martin Newland said the pairing offered qualities suited to driving the newspaper's development, while still maintaining its reputation for quality coverage.
"In Neil, we have a consummate news man and guardian of indispensable Telegraph editorial values. In Will, we have a true innovator with an eye for detail and structural change, attributes that will help me continue to drive development at the title," he said.
His former deputy Sands was appointed editor of the Sunday Telegraph in June as Dominic Lawson was ousted after 10 years in the role.
In other changes on the Daily Telegraph, responsibility for special editorial projects and liaison between editorial, commercial and marketing departments has been handed to managing editor Susan Ryan.
Telegraph Magazine editor Michelle Lavery has been given the additional role of assistant editor of the Saturday edition of the paper.
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