The Tigers will also receive pick 24 from Gold Coast for the 24-year-old, after Prestia nominated Richmond as his preferred destination before the trade period began.
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Prestia played 14 of the first 15 games this season before suffering a season-ending knee injury following a game against Brisbane in Round 16.
The midfielder averaged 25.9 disposals and 5.4 tackles in 2016, which is more tackles per game than any Tiger achieved this season.
Prestia has played 95 games in his AFL career since being drafted with the 9th selection in the 2010 National Draft.