The Ghana international sealed a lucrative season-long deal with the United Arab Emirates club on Saturday, less than 48 hours after informing Sunderland boss Steve Bruce of his desire to fight for his place at the Stadium of Light.
Bruce revealed his frustration after the weekend loss to Chelsea, implying Gyan had moved solely for financial gain.
But Quinn confirmed the club had their reasons for letting their record signing depart.
In a statement on the club's official website, he said: "From the moment Asamoah returned for pre-season training we could tell that there were people trying to move him on. We hoped it would pass by, rebuking approaches from the Premier League, France and Turkey and felt the player would settle back down and continue to help our cause.
"Throughout this time we were also receiving real interest from Al-Ain, but it looked as if that too had lost momentum by last Wednesday.
"Steve spoke to Asamoah on Thursday morning, asking him to knuckle down and we were all set to move on. Later that day however Al-Ain began a prolonged effort to get the deal back on track and this turned the player's attentions once more to a possible move.
"Come Friday, the chairman of Al-Ain and his advisors had flown into Newcastle and arrived at our training ground to discuss a potential deal for Asa.
"They were very professional but determined to sign the player and at this point we took a number of things into consideration: the player's obviously negative demeanour in and around the training ground; the fact that the transfer window in the UAE had over 50 days remaining, meaning this was unlikely to go away; the clear desire of the player to leave; the forthcoming African Nations Cup, which would have meant losing Asamoah for up to six weeks in the new year; the obvious economic benefits to our club in the terms of the final deal laid out to us.
"In the early hours of Saturday morning chief executive Margaret Byrne and myself agreed a loan deal to allow Asamoah his wish to move but that would also, and more importantly, protect the club should things not work out for the player."
Reports this morning suggested Sunderland could receive as much as £6million for the temporary deal, while it was claimed Gyan will quadruple his wages in the Persian Gulf emirate.
Quinn added: "Steve Bruce, our owner and the board all found the football decision that Asamoah wished to make baffling but I, as chairman, with everyone's full support, decided that this deal was in the best interests of our football club.
"There was a lot of things that needed to happen before the deal was fully secured, such as a medical, which has in fact only just been completed today."
Quinn also revealed relations between Bruce and Gyan were again cordial, with the player making a contribution to the club's foundation.
The former Republic of Ireland international said: "Steve's frustrations towards the player, expressed minutes after the Chelsea game, were understandable at such a time but I can reveal that since then Asamoah and Steve have made contact and they are on good terms.
"The olive branch is now there for Asamoah, but he will need to convince Steve, the board and every Sunderland fan of his commitment to this club if he is to return. I am delighted however that he has agreed to make a sizeable donation to SAFC Foundation for each month that he is away on loan.
"It also goes without saying that this puts Steve and his recruitment options in a far stronger position for the January window."
Gyan was unveiled by Al-Ain on Monday morning, stating he was joining an "important club" but refusing to drawn on his long-term future.
The 25-year-old said: "I'm really happy to be here. Al-Ain is an important club and this is a big challenge for me. There will be a lot of expectations on me, but not pressure.
"Everybody who has seen me in the World Cup and at Sunderland knows what I am capable of, but this is a new challenge for me as I'm a new player here.
"We have quality players in the club to win games and do well in the championships. We will try to build a winning team."
When pushed on whether he intended to remain with Al-Ain when his season-long loan deal expires, he added: "I don't promise. I'm somebody who doesn't promise."