Robinho's move to City was made possible after the club accepted a takeover bid by Abu Dhabi United Group on transfer deadline day.
Ribeiro revealed that the deal hung in the balance until just 75 minutes before the window closed at midnight.
"At quarter to 11 at night they asked me, 'Will Robinho play at Manchester City?'.
"I responded that he would play anywhere but Real Madrid."
Ribeiro also claimed: "Meanwhile, [Chelsea chief executive] Peter Kenyon was calling me desperately trying to know what was happening. But I was already certain that Chelsea and Real Madrid would never reach an agreement of more than 40million euros.
"And it was then that I gave the okay to City."