James made six assists and 11 rebounds as the Cavs secured a 4-2 series victory in the Eastern Conference.
They will face either the Golden State Warriors or the Oklahoma City Thunder in the finals.
Oklahoma City lead the Western Conference series 3-2 going into game six of a potential seven on Saturday.
Cleveland have now made the final in consecutive years, while James will be playing in his sixth straight showpiece.
"I knew this was going to be tough game - I just had to bring my game. I had to be in attack mode from the beginning and trust my shots," said the four-time MVP.
"I knew once my shots started going in I could start getting my team-mates involved and they were able to carry me down the stretch."
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LeBron James scored 33 points as the Cleveland Cavaliers beat the Toronto Raptors 113-87 to book their place in the NBA finals.