It took a couple decades, but Ben Affleck and Jennifer Lopez finally have a marriage certificate … and TMZ has the first look.

We obtained the official document from Ben and Jen’s surprise wedding in Sin City, and it shows the couple got married at the famous Little White Wedding Chapel on the Las Vegas strip.

Ben and J Lo’s marriage was performed by Pastor Ryan Wolfe … and they got hitched in front of a witness named Kenosha Booth.

The certificate also has Ben and Jen’s legal names … Benjamin Geza Affleck and Jennifer Lynn Lopez … and shows J Lo wanting to take Ben’s last name and be known as Jennifer Affleck after marriage.

TMZ broke the story … Ben and Jen got their marriage license last month in Clark County, NV and tied the knot after flying into Sin City.

J Lo posted a ton of pics and videos from the surprise wedding, showing her in her wedding dress and Ben in his tux.

Jennifer says they made it to the chapel just before it closed, and that’s reflected in the marriage certificate … Ben and Jen got the marriage license July 16 and the certificate says they were married July 17, with Jen saying it went down a little after midnight.

Ben and Jen spent their honeymoon in Paris, an emotional trip featuring an infamous boat nap and a make-out session in front of their kids, and they’ve got another big celebration on deck.

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