Fletcher, who received the award at the gala ceremony on Sunday evening, played 728 times for the South Coast club in a career that included 121 goals and three promotions.
He finished his playing days on a high, winning promotion to the Sky Bet Championship in 2012/13 and continues to serve the club as head of recruitment and an ambassador.
"The head of our media department phoned me up and told me I'd won, I put the phone down and shed a few tears with the family," he told the club's official website.
"It's nice when you achieve things on the field, but it is so different to achieve things off it when you're old and worn like this.
"For it to be named after Sir Tom Finney is so fitting because my grandad played for England with him.
"Humbled and proud are words that spring to mind, but they don't do it justice."