The Northern Irishman was honoured for the first time at the annual awards dinner in London after he led Liverpool 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.
The 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. SEE MORE AFTER CUT>>>>>>
"For Liverpool and Brendan, I'm sure we all hope this season marks the beginning of a new voyage and a new era."
The Crystal Palace manager, Tony Pulis, was named the Barclays Premier League manager of the year for his work at Selhurst Park, which saw the club keep their top-flight status after he guided them to an 11th-place finish.
Pulis arrived at the club when Palace had four points from 11 games but they finished the season with 45.
He told his club's official website: "This is a community club, based in the most densely populated area in London and has a great opportunity of pushing forward.
"We've got to stay in the Premier League for the next two or three years to realise what we can eventually achieve. We have to look forward and say this is the way we will go and do it."
Leicester City's manager, Nigel Pearson, won the Sky Bet Football League Championship manager of the year award after he steered the Foxes to automatic promotion to the top flight, while Wolves' Kenny Jackett and Leyton Orient's Russell Slade were named joint League One managers of the year.
Scunthorpe's Russ Wilcox picked up the League Two award, with Sheffield United's Nigel Clough named the FA Cup manager of the year.
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