After four years as consultant editor at the Mail, Bryant will handle the long-term direction of The Daily Telegraph and The Sunday Telegraph, working closely with respective editors Martin Newland and Sarah Sands.
Fletcher was obliged to step down in June because of a conflict of interest rule, which came into force when his wife Sands was promoted to Sunday Telegraph editor.
Murdoch MacLennan, chief executive of the Telegraph Group, hailed his former Associated Newspapers colleague's long newspaper career.
"John has enormous experience as a very senior executive at both The Times and the Daily Mail. He will support the editors and help map out the way forward for both newspapers," he said.
Bryant was executive editor of the Daily Mail in the 1980s, before joining The Times as managing editor in 1986. He was promoted to deputy editor, a role he returned to after editing the Sunday Correspondent and The European.
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