The American midfielder agreed terms on a three-year deal and passed a medical and is set to leave Rangers to join the Potters for an undisclosed fee in the coming days.
Edu has agreed personal terms with the Potters and passed a medical over the weekend, but is unlikely to complete his switch in time to face Wigan Athletic on Saturday.
Stoke can now finalize the 26-year-old's work permit application before confirming his acquisition for an undisclosed fee.
Tony Pulis' team have already signed two of Edu's teammates this summer in former Rangers star Jamie Ness and fellow U.S. international Geoff Cameron.
Stoke drew 1-1 with newly-promoted Reading on the opening day of the Premier League season before holding Arsenal to a 0-0 tie at the Britannia Stadium on Sunday.
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