Odegaard joined Arsenal on loan from Real Madrid towards the end of the January transfer window.
He is yet to register a goal or an assist in eight outings for the Gunners, prompting former players like Martin Keown and Nigel Winterburn to criticise his start.
But Arteta has been highly impressed by the 22-year-old and is thrilled with how well he has settled, amid speculation over whether Arsenal will opt to pursue a permanent move.
"I'm really happy with him," said Arteta. "I think he has settled really, really quickly into the team and with what we demand from the players.