Fatih Terim's men fought back from a goal down to lift the Turkish top-flight crown for the second time in a row.
Rijad Bajic's effort in the 17th minute broke the deadlock at the Turk Telekom Stadium to put Istanbul Basaksehir ahead but the hosts proved their resilience in the second half.
Two minutes after the restart, Feghouli scored the equaliser for Galatasaray before Onyekuru grabbed the match-winning goal in the 67th minute.
Galatasaray won the league after gathering 69 points from 33 games, three points more than Istanbul Basaksehir with a game to go. When points are tied, the Turkish league uses the head-to-head record instead of goal difference so Galatasaray's title is confirmed.
Fatih Terim's men will hope to end their campaign on a high when they visit Sivasspor for their last league outing of the season on May 25.
On the international scene, Onyekuru has been named in Nigeria's 25-man provisional squad for the 2019 Africa Cup of Nations while Feghouli is expected to play a part in Algeria's campaign at the continental showpiece.