Gibbons, 18, took the test after a youth team match against Aston Villa in September, but it has only been announced after the FA and Sunderland concluded their investigations.
Sunderland said: "A club investigation also took place at the time and his scholarship with Sunderland was cancelled with immediate effect."
Gibbons has also been suspended from football for two years, backdated to mid-October, when he was provisionally suspended.
The club criticised their former youth team captain's conduct but added the player has been given support for the future.
"Lewis not only let our club down, he let himself and his team-mates down massively," Sunderland academy manager Ged McNamee said.
"We took the strongest possible action in terminating his contract as every player knows the severe consequences.
"We have, however, worked to ensure that support and assistance was available to the player and his family through what has undoubtedly been a difficult and challenging time for them."