The Dubai-based club, who have been searching for a top-quality striker after finishing seventh in the 2014/15 UAE Pro-league, made the announcement on their official website.
Al Ahli chairman Abdullah Al Naboodah took to Twitter to announce that the details of Adriano's contract and medical report will be made public in the next couple of days.
However, Shakhtar CEO Sergei Palkin told football24.ua that the deal has not been completed just yet. Palkin refused to divulge the fee Al Ahli have agreed to pay, and added that negotiations have already taken place.
Adriano scored 21 goals for Shakhtar in all competitions last season, nine of which came during the Champions League, with the Brazilian becoming the first player to score four first-half goals during Shakhtar's 7-0 thrashing of BATE Borisov in October. In the same match, he also broke the record for the fastest Champions League hat-trick.