Fifteen-year Ogilvy stalwart Anderson -- a US national -- will join on November 1 as group director of communications.
He will report direct to Sky CEO James Murdoch and will have overall control of corporate communications, programme publicity, public affairs, CSR and internal communications.
He will join as BSkyB bids to keep hold of its rights to broadcast FA Premiership live football matches. It is also chasing 10m UK subscribers by 2010.
"I am sure he will help us build Sky's reputation as the nation's number one entertainment choice," Murdoch said.
Anderson replaces Julian Eccles, who is to leave the broadcaster after five years. He is not thought to have accepted a new position.
Eccles "will be hands-on, assisting with the transition" Sky said in a statement.
News of the highly regarded Anderson's exit is a major blow to Ogilvy, which also lost former European CEO Paul Barber earlier this year. Barber quit to join Tottenham Hotspur FC.
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