Greening, who has played in every minute of Boro's season so far, polled 34% of votes ahead of Geremi (26%) and Gareth Southgate (23%).
The former Manchester United star has impressed this term with his all action displays in a reshaped midfield after a shaky start to his Boro career last season.
He said, "This means a lot because the fans have voted for me. It is a great achievement."
He received his prize in a ceremony on the Riverside pitch before the Tottenham game on Saturday.