The 6-foot-10 center started Orlando's final 53 games and appeared in 80 overall last season, averaging 10.5 points, 3.3 rebounds and 1.2 assists in 21 minutes per game.
He attracted interest from several teams as a free agent, including the NBA champion Lakers, who offered him a six-year, $17 million deal last month.
But Amaechi, who played three seasons overseas before joining the Magic last year, opted to remain in Orlando because the team gave him a chance to play when no other NBA team offered him an opportunity.
The 29-year-old center can make more in a multiyear deal with the Magic than with the Lakers as much as $27 million over six years but not until after this season.
Because of salary cap rules, the Magic was only able to increase Amaechi's salary 20 percent for the upcoming season $450,000 to roughly $600,000. The Lakers could have paid him $2.2 million in the first year of a deal.
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