The 26-year-old Ghana international, who spent most of last season on loan at the club, has sealed a transfer on undisclosed terms.
Al-Ain are reported to have paid £6million ($9.3m) for Gyan's temporary stay and will hand over a similar fee to secure his services on a long-term basis.
A Sunderland statement said: "Sunderland AFC can confirm that Ghana international Asamoah Gyan has joined United Arab Emirates side Al-Ain on a permanent deal.
"The striker initially joined the recently-crowned Etisalat Pro-League champions on loan in September 2011 but will now remain in the Gulf state after the clubs agreed undisclosed terms."
Gyan joined Sunderland in a £13million-plus move from French side Rennes just weeks after starring for his country at the 2010 World Cup finals in South Africa, where his extra-time penalty miss against Uruguay cost them a place in the last four.
The African scored 11 goals in his first season in English football.
He moved on loan to the UAE club in September last year and scored 22 goals as Al-Ain claimed the league title.
Source: AFP
Source: AFP