The versatile winger agreed to join the Minstermen on June 1 and, having been away with his country, has now put pen to paper on his two-year deal.
Puri, 25, joined Scottish club St Mirren in March on a deal until the end of the season but made just two appearances
Speaking earlier this month, York boss Nigel Worthington said: "He's a wide player who can play on the right or left.
"I remember him playing against us when I was manager of Northern Ireland and, being in the same group, we obviously watched Estonia several times and I've looked back at my reports from then.
"He's 5ft 9in tall and, when I was talking about our need for tall players not preventing us from signing a good, small one, he falls into that category."