Pudil, who returns to the country he has earned 35 caps for, made 91 appearances for Owls, signing from Watford for £1.5m after a successful loan move during the 2015/16 season.
The 33-year-old left-back, who can also deputise on the wing, scored four goals for Wednesday.
He leaves on a free transfer as part of Steve Bruce’s spring-clean of the Wednesday squad after the manager voiced his desire to reduce the number of first-team players.
FK Mladá Boleslav play in the Czech first division, where they finished seventh last season.
In May Pudil sent a message to the S6 faithful on social media announcing his departure.
He said: “So I'd like to thank all my teammates, managers, employees and fans, that I had a chance to meet during my four - years - at Sheffield Wednesday Football Club.
“I was honest to wear this beautiful shirt every time I stepped on football pitch and I'm really glad I’m part of this family! I'll never forget it!
“But it's time to say goodbye, but I’m sure I'll be near by Sheffield, so I’ll see you in the city or at the stadium sometime.
“I want to wish you all the best in the future to end where you belong and that's premier league! This massive club deserves to be there, and you all Sheffield Wednesday fans as well!!!”