The Portuguese club released a statement saying Arsenal would pay an initial 35m euros (£29.9m) for Vieira with the rest in potential add-ons.
Vieira, 22, has yet to win a senior cap for Portugal but was voted player of the tournament at last year's European Under-21 Championship.
He provided 14 assists in the Primeira Liga last season.
Vieira also scored six goals in 27 league outings as he helped Porto claim the top-flight title in Portugal.
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