The out of contract 24-year-old was not offered a new deal by the Lions after 107 goals in 81 games.
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“It is disappointing when any player departs, and Josh has given great service to our Club,” Football General Manager David Noble.
“We thank him for his time at the Club and wish him all the best for his future.”
Green was recruited from Tasmania with pick 32 in the 2010 National Draft.