The Czech pair have joined from Granada and Udinese respectively following the takeover of the Hornets by the Pozzo family (who own the aforementioned clubs) and appointment of Gianfranco Zola as manager.
26-year old winger Pudil is keen to head back to Vicarage Road following a previous trial whilst 20-year old striker Vydra is excited about competing in England's second tier.
"I did not have to think twice (about joining Watford)," Pudil told chovanecsport.cz.
"I came here five years ago on trial and loved it. I'm also looking forward to playing under Gianfranco Zola."
Vydra added: "I see this as a big opportunity and I can't wait to play.
"Watford is in London and the second division in England is a great competition."