Puri, who could win his 50th cap for his country in Monday's friendly against Belarus, will join the League Two club on a two-year contract subject to a medical.
The 25-year-old has become manager Nigel Worthington's fourth summer signing following the arrivals of Ryan Jarvis, Craig Clay and Ryan Bowman.
"He's a wide player who can play on the right or left," said Worthington.
"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.
"He had a trial period at Kilmarnock last season and I have spoken to Jimmy Nicholl about him.
"Jimmy said he was excellent and could not fault him on anything so I asked him why he didn't sign him and he said that they had a young lad coming through the system who was a similar player and they did not want to block his progress so Sander went to St Mirren instead."
- Sports & Recreation
- Nigel Worthington
- Ryan Jarvis