The financial details of the deal were not disclosed.
Founded in 2015 by twin brothers Swapnil Shinde and Snehal Shinde, Mezi will now operate as a wholly-owned subsidiary of American Express.
Mezi, which is also backed by Nexus Venture Partners, uses artificial intelligence (AI) and human expertise to personalise online travel discovery and booking experience.
"Mezi's AI-powered experience opens up exciting new ways for us to connect with and serve our card members and creates opportunities for us to build more meaningful relationships with them," Phil Norman, vice president of American Express Digital Labs, said in a statement.
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"We've built Mezi to become better with each and every interaction and based on the success of our pilot with American Express, we are excited to bring Mezi's mobile capabilities to more Card Members," Snehal Shinde, co-founder and CTO of Mezi, said.
The co-founders will continue to lead Mezi, and will report to Phil Norman, vice president at Amex Digital Labs, Global Consumer Services Group at American Express.