The Polish side will pay £3.5 million to secure the forward. The deal is Celtic’s first official business of the summer.
Palma had spent the season on loan with Poznan, who have now exercised their option to buy.
The decision came after Sevilla were reportedly interested in Palma.
Poznan’s president, Karol Klimczak, said: “It’s clear that we want to keep Luis Palma.
“We’re working on it. We want to sign him, it’s not easy, but we want to.”
Lech director, Adrian Gałuszka, added: “It’s no secret that Luis feels good in Poznan.
“He was a magician this season, put in important numbers and contributed to several important team results.
“We have to wait for the final decisions, which I suspect will be in the coming days.”
Palma has signed a three-year deal with the club.