Westerveld, who will be 37 years old in October, will replace goalkeeper Hans Vonk, who retired at the end of last season aged 41.
Ajax, runners-up in the South African league in May, is the 11th club of Westerveld's nomadic career that has seen him play in the Netherlands, Spain and Italy.
Westerveld, who made six appearances for his country, turned out 75 times for Premier League side Liverpool during a three year spell.
He will miss Ajax's opening game of the season this weekend but is expected to debut next Wednesday.
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