The United States international has been a long-standing target of City boss Tony Pulis and last weekend agreed terms on a three-year deal and passed a medical.
The only hold-up was his work permit and, with the club confirming on their official website on Thursday morning that the Football Association have given approval for them to proceed with that, the move looks set to go through.
Stoke have cautioned, though, that the 26-year-old is unlikely to be available for the weekend clash with Wigan owing to the timescales involved.
Edu is a 37-cap international for the States and spent four seasons with Rangers following a move from Toronto FC, winning three league titles and making 125 appearances for the club.
Referring to Edu, Stoke assistant manager Dave Kemp said on Thursday morning: "He has been granted the work permit, but as usual, there are other bits of paper that have to be stamped and marked.
"He has another appointment tomorrow, I think with the Border Agency just to clarify that.
"But he has been granted the work permit, so hopefully we are very close to getting that over the line."
Source: PA
Source: PA