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The 33-year-old was due to move to Murrayfield on a two-year contract after the World Cup.
However he agreed the move before the change in ownership, with the club having been returned into Scottish Rugby Union hands last month at the end of a bitter dispute with the former franchisees.
The SRU confirmed the contract Larkham signed was with Edinburgh Rugby Ltd, the company set up by Bob and Alex Carruthers, and had not passed into the union's hands after the brothers' five-year franchise was cut short after just one season.
Guinness Premiership newcomers Leeds announced this week that they want to sign Larkham, and they will now be free to negotiate with the 101-times-capped international.
Edinburgh chief executive Nic Cartwright said: ``The situation has been complex with a contract having been signed in the summer months between Stephen Larkham and the previous owners of the Edinburgh Rugby franchise.
"This contract remained with Edinburgh Rugby Ltd and after discussions with that organisation Stephen has opted to secure a new playing contract elsewhere. Obviously we wish him well with his next move.
"Meantime, we'll press ahead with our own plans to strengthen our squad and we'll be commencing interviews for a new head coach in the near future.''
Leeds have restricted their recruitment for the new season largely to National League players but have set aside a budget for a big-name signing, and Larkham would fit the bill.
He has played in the last two World Cup finals and won two Tri Nations titles as well as two Super 12 medals with the ACT Brumbies.
With Australia likely to reach the semi-finals of the World Cup, Larkham would almost certainly miss the first six league games of the season
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