The attacker has penned a deal to 2029.
"It's an incredible environment and the best possible place to be for a young player," Bobb said.
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"To know I'm going to be here at the club until 2029 means everything to me.
"Now I just want to focus on continuing to further my development and to work as hard as I can every day to try and help the club achieve more success."
City director of football, Txiki Begiristain added: "Oscar is blessed with superb natural talent and technique and has already established himself as a very important member of the squad."