The 26-year-old has signed a three-and-a-half year contract with the team from Konya who sit seventh in the country's Super Lig.
Douglas told the club website: "I'm very excited, very happy. I have opened a new chapter in my career."
He said his goal was to help his new side qualify for the Europa League.
Douglas helped Lech win the Polish title for a seventh time last season, but they presently lie sixth in the Ekstraklasa.
Konyaspor manager Omar Korkmaz Metropolitan said he hoped the Scot would force his way into the side by continuing the form he showed with the Poles.
Douglas began his career with Queen's Park and moved to United in the Scottish top flight in 2010.
He switched to Poland after three years at Tannadice.
Former Dundee United left-back Barry Douglas has completed his transfer to Turkish top-flight club Torku Konyaspor from Lech Poznan.