The deal is for one year at $1.27 million, sources told ESPN.com.
Udrih will back up starter Raymond Felton along with veteran guard Pablo Prigioni, who re-signed with the Knicks earlier this summer. Udrih will fill the spot on the roster vacated by Jason Kidd, who retired to become the head coach of the Brooklyn Nets.
"Beno is a solid addition to our backcourt where he will give us more depth and flexibility," Knicks general manager Glen Grunwald said. "He is a talented and experienced floor general who brings championship experience to our locker room."
The lefty Slovenian played well for the Orlando Magic at the end of last season after he was acquired from the Milwaukee Bucks. He averaged 10.2 points and 6.1 assists in 27 games for the Magic. Overall in 66 games in Milwaukee and Orlando, the nine-year veteran averaged 8.2 points and 4.6 assists on 44 percent shooting.
According to a league source with knowledge of the decision, Memphis was a strong suitor and Philadelphia also showed interest in Udrih, whose deciding factor was his chance to win with the Knicks.
The Knicks had limited options in free agency this summer because of their salary-cap position but have added Metta World Peace and Udrih. Earlier this week, they signed big man Jeremy Tyler to a partially guaranteed contract. The Knicks also re-signed J.R. Smith, Kenyon Martin and Prigioni. They traded for big man Andrea Bargnani.
The Knicks now have 14 players under contract, and the Udrih deal will push their luxury tax bill to more than $32 million and their total payroll to $119.8 million, including taxes.
Information from ESPNNewYork.com's Ian Begley was used in this report.