The 24-year-old is currently on international duty with Poland, but underwent a medical in Warsaw before putting pen to paper on the deal.
The winger initially joined Verona on loan before making his switch from Sampdoria permanent earlier this year.
"Pawel's arrival is another positive step in the right direction for us. He's a Polish international with good pedigree who will bring quality to the side," manager Jimmy Floyd Hasselbaink told the club's official website.
"He is versatile, can play on either the left or right, and works tirelessly for the team. He's a very hardworking player. I'm really looking forward to working with him and adding him to the squad."
Wszolek becomes QPR's eighth signing of the summer.