The 32-year-old Romanian captain recently joined the Hammers on a one-year deal from Shakhtar Donetsk.
"For me it's an honour to wear this shirt and to play in the Premier League," Rat told the club's official website. "I will be very proud to wear the claret and blue colours and I hope to satisfy the fans.
"I'll be very excited when I pull on the kt for the first time, because it will be my first game here."
West Ham get their Premier League campaign started at home to Cardiff City on August 17.