The American international arrives at the Potters following the finalisation of work permit details, and will compete for a place in central midfield in Tony Pulis' side
The United States international midfielder had earlier this week completed a medical and agreed terms on a three year deal with the Potters, but was waiting for details of a work permit to be finalised.
Edu announced on Twitter: "Stoke City, it's finally official! Excited & looking forward to this next chapter in my career. Thanks for all your well wishes & support!"
The 26-year-old combines stamina with technique and can also play at centre back, and played at the 2010 World Cup for the United States, for whom has won 37 caps.
The Potters earlier today completed the signing of Charlie Adam from Stoke, and the pair are set to compete for one of two central midfield spots with Dean Whitehead, Glenn Whelan, Wilson Palacios and fellow American arrival Geoff Cameron.