The 27-year-old, who has a contract with PSG until 2023, spent last season at Real Madrid behind Belgium number one Thibaut Courtois.
Areola, who lifted the World Cup in 2018, has won three French league titles during his time at the Parc de Princes.
The Cottagers have also signed the likes of Brighton striker Anthony Knockaert and Southampton midfielder Mario Lemina ahead of their return to the Premier League.
They will host Arsenal on Saturday in their first game of the season.
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