The 25-year-old Ghana international will join Al-Ain after becoming unsettled on Wearside barely a year after his switch from Rennes to the Stadium of Light.
Manager Steve Bruce said: "Anyone who has seen Asamoah play will know that he hasn't been himself in recent months. This option suits all parties at the present time and the club is well-protected in the deal.
"Asamoah has three years remaining on his contract and of course my wish would be that he finds his spark again and we see him in red and white stripes next season in the form that first attracted us to him."
Gyan arrived at the Stadium of Light last summer after starring for his country at the FIFA World Cup™ in South Africa, and was a big hit on Wearside, scoring 12 goals.