The Northern Irishman was honoured for the first time at the annual awards dinner in London after he led the Reds to second place in the Barclays Premier League, which was the club's highest finish in five years.
The award is voted for by all LMA members, including every manager from the top four professional leagues in English football.
LMA chairman Howard Wilkinson said of Rodgers' win: "There can be no greater tribute to a manager and his work than a tribute awarded by his match day foes and peers. This evening we applaud Brendan Rodgers as he receives that most valuable award.
"Liverpool Football Club's performances and results this season have provoked memories of some of those momentous years in the past when they had to contend with those two United's, the first from Leeds, the second from Manchester.
"For Liverpool and Brendan, I'm sure we all hope this season marks the beginning of a new voyage and a new era."