The 28-year-old Dutch international signed a long-term contract, Spartak said on their website.
"I knew Spartak as a very strong side, they beat us twice this year," De Zeeuw told Russian media, referring to two Ajax defeats by Spartak in the Europa League last 16 tie in March.
"And it has played a part in my decision to move to Moscow."
Financial details were not disclosed but local media have put the transfer fee at six million euros.
De Zeeuw is the first major signing for the nine-times Russian champions during this transfer window.
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