The Nigerian marksman played with the current City coach Benni McCarthy at the Hammers, and it's no surprise that he has decided to sign.
The 30-year-old joins the Mother City-based club as a free agent having last featured for German club Darmstadt 98 last season.
The Citizens confirmed his arrival on their social media platforms on Tuesday night.
He also made 48 appearances for the Super Eagles of Nigeria between 2005 and 2014.
Obinna is seen as a direct replacement for Lebogang Manyama, who joined Turkish side Konyaspor last week.