The Ghana international signed for the UAE outfit on Saturday having only moved to the Stadium of Light in August 2010 for a club record £13 million.
The 25-year-old had fallen out of favour with manager Steve Buce after a series of disappointing performances and a return of 11 goals in 37 appearances in his 13 months in the Premier League.
Bruce had expressed his frustration at Gyan's decision, suggesting his main motive for the switch had been financial gain.
But Sunderland chairman Niall Quinn confirmed that the club had had sound reasons for letting Gyan leave.
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."
Quinn then listed the reasons behind the deal, including Gyan's negative attitude, his clear desire to leave; January's Africa Cup of Nations, and the financial benefits.
Reports suggested Sunderland could receive as much as £6million for the temporary deal, while it was claimed Gyan will quadruple his wages in the Gulf emirate.
Quinn 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: "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."