The 27-year-old has made only one Premier League appearance for the Potters since joining them from Rangers in the summer of 2012.
Mark Hughes's appointment as manager has not changed his fortunes and the Britannia Stadium outfit are happy for him to leave for Philadelphia, who see Edu's arrival as a coup for both them and the division.
"As a US international with experience playing against some of the best competition in the world, Maurice adds a wealth of knowledge, skill and leadership to our club while still being in his prime," Philadelphia's team manager John Hackworth told the club's official website.
"We think he will be an excellent addition to our squad and we are very excited to have him return to MLS and represent the Philadelphia Union."
Edu, who has been capped 45 times by the United States national team, previously played in the MLS for Toronto FC, soon to be Jermain Defoe's new club, during the 2007/08 season.