During the September-to-September voting period, Ashwin took 48 wickets and scored 336 runs in eight Tests.
The spin-bowling all-rounder, who starred in India's 4-0 Test series victory over England, was also named Test cricketer of the year for the voting period, which covered the 12 months to September 20.
He becomes only the third Indian player to win the prestigious Sir Garfield Sobers Trophy, following in the footsteps of batting greats Sachin Tendulkar (2010) and Rahul Dravid (2004).
"It feels great to follow the likes of Sachin Tendulkar and Rahul Dravid in being named as the ICC cricketer of the year," Ashwin, 30, said in a statement.
"To also win the ICC Test cricketer of the year makes it even better."
During the September-to-September voting period, Ashwin took 48 wickets and scored 336 runs in eight Tests. He also snared 27 Twenty20 international wickets.
The Chennai native consolidated top spot in the International Cricket Council (ICC) Test bowling charts after he took a series-leading 28 wickets in the five games against England, which wrapped up this week.
Quinton de Kock, South Africa's wicketkeeper-batsman, was named one-day international cricketer of the year after he scored 793 runs in 16 50-over games.
And the West Indies' Carlos Brathwaite won international Twenty20 performance of the year for his 10-ball 34 not out, including four sixes in the final over, to clinch a stunning victory over England in the World Twenty20 final.