The 64-year-old Italian, who led Leicester to a 5,000-1 Premier League title triumph, becomes only the second non-Briton to win the award after Arsenal’s French manager Arsene Wenger, who was honoured in 2002 and 2004.
Ranieri, who was also crowned Premier League Manager of the Year, collected the award at a ceremony in London on Monday after a helicopter ride from Leicester’s Premier League victory parade.
“As a player I was not a champion, but I had great heart,” he told the audience.
“I told my players I wanted them to play English football and I put my little Italian tactics with their English heart and then we can do something special.
“They followed me. It is a fairytale and I don’t know what has happened. I don’t know, believe me.”
Ranieri was also named Italian Manager of the Year in his homeland last month.
He succeeds Bournemouth’s Eddie Howe, who won last year’s prestigious LMA award after steering Bournemouth to promotion from the Championship for the first time in the club’s history.
“My congratulations go to the LMA manager of the year sponsored by Barclays, Claudio Ranieri, who, in his first year as manager of Leicester City, has achieved the most astonishing of sporting triumphs,” said LMA chairman Howard Wilkinson, the former Leeds United manager.
“He thoroughly deserves all the recognition and praise being bestowed upon him tonight.”
Ranieri was due to fly to Thailand with his squad on Tuesday for a post-season trip to the country of the club’s owners, travel retail group King Power.