The 29 year-old's winning goal was scored in February for Penang against Pahang in the Malaysia Super League, an unstoppable free-kick which swerved incredibly and flew into the top corner.
Subri was named as the winner at Tuesday's (AEDT) ceremony in Zurich, beating Marlone and Daniuska Rodriguez.
"Honestly it never crossed my mind that I would be at this level and be able to stand with world-class players," Subri said. "I would like to say thank you to my team, my coach, my family, my father, my mother and all the people who voted me - thank you very much."
There were initially 10 candidates to win the vote, which decides the best goal between September 30 2015 and September 30 2016, before they were narrowed to three.
Subri polled 59.5 per cent, ahead of Marlone with 22.86 per cent and Rodriguez with 10.01 per cent.
The rest of the vote was made up of 7.68 per cent, which came for the other goals before the list was narrowed down.
Marlone scored a magnificent goal for Corinthians in a Copa Libertadores match against Cobresal in April, controlling a cross with his chest to set himself up for an acrobatic volley.
Rodriguez's strike came for Venezuela in the South American Under-17 Women's Championship in March, with her amazing dribble bamboozling defenders Sofia Montoya and Manuela Venegas before she delivered a thumping finish.
Lionel Messi, Neymar and Hal Robson-Kanu were among the players to miss out when the field was cut down.
Fans from around the world had the opportunity to vote on FIFA's website and across social media, with the award named in honour of Real Madrid legend Ferenc Puskas.
The 2015 award had been won by Wendell Lira of Goianesia, while Real Madrid's James Rodriguez won in 2014 after a goal at the World Cup for Colombia against Uruguay.