James, undisputed as the sport's best current player, scored a game-high 37 points and grabbed 12 rebounds in Miami's 95-88 Game Seven win.
The 28-year-old also won the award last year when Miami beat the Oklahoma City Thunder to win the championship and he has swept all the major awards in the past two seasons.
Four times in the last five seasons, including each of the last two, he has been named MVP during the regular season, elevating him among the greatest players the game has seen.
James, who was widely criticised in the United States after leaving his former team Cleveland Cavaliers for Miami in search NBA championship rings, received the award from Boston Celtics great Bill Russell.
"I'm blessed," James said at the trophy presentation. "What everyone says about me off the floor doesn't matter."