They lost 2-0 at home to Nottingham Forest in the first leg of their semi-final last Friday, which they will need to overturn at the City Ground in the second leg this week.
"The award has been well earned," said Glovers chairman John Fry.
"Russell came to Huish Park last June, and at short notice put a team together and has produced the goods.
"He caught the imagination of the league in the way he has done it. We have been near to the top of the league all season, and without a question of doubt he deserves this recognistion."
Sir Alex Ferguson was named Premiership manager of the season, with Sunderland's Roy Keane honoured in the Championship and Hartlepool's Danny Wilson took the League Two prize.