The United States international initially moved to the Britannia Stadium in 2012 from Rangers but struggled to make an impact in the Premier League - making just one substitute appearance for Stoke in October that year.
Loan spells at Bursaspor and Union followed, with the 28-year-old returning to the league he started in with Toronto FC.
Edu - named in the MLS All-Star Team during his recent loan spell at PPL Park - moves ahead of the new MLS campaign and explained his delight at returning to Philadelphia.
"I couldn't be happier to permanently return to Philadelphia and to play in front of our great fans," he told the club's official website.
"I believe in this team's future and am excited to be an integral part of that."
Union get their MLS season under way on March 7 against Colorado Rapids.
