In 2013, the rapper surprised his then-girlfriend with a private party at AT&K Park, where he proposed to her in front of her family and friends.
While the happy moment was filmed for an official online video as well as for "Keeping Up With the Kardashians", amateur video of it made its way to video websites including YouTube, reported E! Online.
The couple sued YouTube co-founder Chad Hurley, whose new website MixBit's logo was seen on the fuzzy footage.
"With Mr. Hurley's settlement payment, we believe a fair and just outcome has been achieved," Kardashian and West's lawyer said.
The couple alleged that Hurley "tagged along with someone who was invited" to the party and was allowed to stay after signing a confidentiality agreement, prohibiting him from posting videos or images.
They sought unspecified damages for alleged breach of contract, fraud and unjust enrichment.