Stoke have today confirmed that they have agreed personal terms with the 26-year-old American international.
The transfer is now subject to Edu passing a medical over the weekend and then being granted a work permit.
The American international made 125 appearances for the club, scoring 12 goals in the process.
Signed by Walter Smith in August 2008 from MLS side Toronto FC, he collected SPL winner's medals in each of his first three seasons in Glasgow.
Arguably his most memorable individual moment in a Rangers shirt was the injury time winner against Celtic in February 2010 that sent the Light Blues 10 points clear of their rivals with a game in hand.
As well as three league championships the 26-year-old leaves Glasgow with two winner's medals from the League Cup.
He was a second half substitute in the dramatic 2010 final that saw Rangers defeat St Mirren with just nine men.
And he played the full 120 minutes a year later as Rangers clinched an extra time win over Celtic at Hampden.
Edu has not featured for Ally McCoist's side this season but has turned out for the USA in an historic 1-0 win over Mexico at the Azteca Stadium.