As head of BBC TV News since January 2000, Mosey was responsible for all output across the One, Six and Ten O'Clock News, Newsnight and News 24.
Previously, Mosey was controller of Radio Five Live and a former editor of Radio 4's 'Today' programme.
It is not known who else went for the job, but BBC Radio Five Live controller Bob Shennan had been tipped as the top contender.
Mosey will be responsible for developing and strengthening sport's multi-media, multi-platform services and spearheading BBC Sport's move to Manchester in 2009.
However, that move could now be blocked by the board of governors, because of London's successful 2012 bid.
BBC Sport currently has a large rights portfolio, including the rights to the World Cup up to and including 2014, the Olympics up to and including 2012, Wimbledon, Six Nations, The Open Golf, the FA Cup, Premier League highlights football and the Grand National.
Mark Thompson, BBC director-general, said: "Mosey's experience and passion will be invaluable in leading the Sport Division through its imminent and long-term challenges."
Salmon announced he was quitting in April after five years at the helm of BBC Sport and eight years at the corporation, to take on the chief executive role at the Rupert Murdoch-owned independent production company The Television Corporation.
During his five-year tenure, Salmon was responsible for securing the Six Nations Rugby, the FA Cup, football highlights for 'Match of the Day', The Derby, The Open Golf, Wimbledon and The Grand National among others.
More recently, he won the UK rights to cover the 2010 Winter Olympics from Vancouver and 2012 Games and he brought in a record-breaking 11m viewers for the 2004 Athens Olympics on BBC One last year.
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