AP
The couple said in a joint statement obtained by the Post: "We regret that our marital relationship has come to an end and we have agreed not to make any other public statement on this subject."
The Post reported earlier this week that Spitzer is dating New York City Mayor-elect Bill de Blasio's spokeswoman, 31-year-old Lis Smith.
Eilot and Silda have been married since 1987 and have three daughters together, according to the New York Daily News. They've been living apart for months.
Spitzer resigned his position as governor in 2008 amid a prostitution scandal, during which his wife stood by him.
Spitzer ran for city comptroller earlier this year but lost in the primary.