"I've had eight good years at Sunderland, the club has been tremendous to me and have worked hard to keep me, but this offer has been a dream come true," Sbragia told the club's official website.
"It has taken two tortuous days to come to this decision and only time will tell whether this has been the right one.
"I'd like to thank Sunderland for the opportunity they have given me. I feel that the club are in a good position now and will do well under the new management team."
Sunderland boss Howard Wilkinson said: "I'm very, very disappointed to lose Ricky.
"In the time that I've been here I have come to see him as an extremely valuable member of staff, this has been proven by my efforts to keep Ricky, but I understand his desire to pursue a dream.
"Obviously this leaves a hole in the staffing arrangements which I will need to address in the short term, but there is still too much going on to undertake a full appraisal of our long-term staffing requirements."
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