Former champions McLaren, who had their worst ever season in 2015 and have not won a race since 2012, already have a reserve driver in Belgian Stoffel Vandoorne.
Matsushita, 22, will concentrate on work in the team's simulator to support race drivers Jenson Button and Fernando Alonso while also competing in the GP2 feeder series.
There are no Japanese drivers currently in Formula One.
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"To step into the world of Formula One fulfils a boyhood dream, and is a huge step forward in my career," he said.
(Reporting by Alan Baldwin, editing by Amlan Chakraborty)
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