Six Nations chiefs confirmed the former England captain's appointment at their meeting held in Rome.
Beaumont's three-year term of office begins immediately and he succeeds Welshman David Pickering, who will remain on the council as Welsh Rugby Union representative.
Beaumont said: "It is a privilege to be involved with the biggest annual rugby competition in the world.
" I would like to thank the outgoing chairman, David Pickering, for his work over the last four years, and I look forward to working with him and the rest of the council."
Ireland's Pat Whelan was elected as Six Nations vice-chairman, also with immediate effect.
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