The 23-year-old former Queen's Park defender, who has made 75 appearances for United during his three seasons at Tannadice, was out of contract next month and available on a free transfer to clubs outside Scotland.
His deal also includes the option of extending his stay with the six-times Polish champions for a further 12 months.
Poznan's sporting director Piotr Rutkowski said: "We like innovative solutions and that is why we decided to look for new players who are fairly unknown in the Polish market.
"We've been watching Dundee United for the past two years now while we've been looking for a left-back and I knew that someone like Barry Douglas could fit in here.
"The transfer has been completed relatively quickly because Douglas had ended his contract with United and he did not have to negotiate with his club, which often delays the transfer."
Lech Poznan are currently second in the Ekstraklasa, the Polish top flight, six points behind leaders Legia Warsaw with two games to play.