Sanchez has scored 20 goals for Arsene Wenger's men in 2015 and the Chile star is the third consecutive player from South America to land the prize, which was first awarded in 2013, following in the footsteps of Luis Suarez and Sergio Aguero in winning the award.
The 26-year-old beat off competition from Jamie Vardy, Aguero, David De Gea, Harry Kane and John Stones and spoke of his joy at earning the accolade.
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"I'm delighted to receive the FSF Player of the Year award. Personally, it's been a great 2015 for me on the pitch with both my club and country," Sanchez, who also helped Chile to Copa America success earlier this year, said.
"Arsenal have enjoyed a good start to the season and it was disappointing to pick up an injury. But I'm hoping to be back soon to help my team-mates have another successful year."
Wenger added: "Alexis has had a great 2015 - winning the FA Cup with us and the Copa America with Chile.
"He has made a huge impact on English football since his arrival at the Emirates Stadium and I'm very happy that his skill, ability and dedication has been recognised by football fans across the country."