The Grizzlies announced the deal Tuesday. Terms and length of the contract weren't disclosed.
Udrih, 31, averaged 4.9 points, 1.4 rebounds, 2.8 assists and 15.7 minutes in 41 games with the New York Knicks and Grizzlies last season. He played 10 regular-season games for the Grizzlies, who claimed him off waivers on Feb. 27.
In the Grizzlies' Western Conference playoff first-round loss to Oklahoma City, Udrih averaged 7.9 points, 1.7 rebounds, 1.7 assists and 16.4 minutes.
Udrih has career averages of 8.8 points, 2.2 rebounds and 3.6 assists in 10 seasons with the San Antonio Spurs, Sacramento Kings, Milwaukee Bucks, Orlando Magic, Knicks and Grizzlies. He played on San Antonio's 2005 and 2007 NBA championship teams.