The Gunners completed a £70M deal to land the Brazil international earlier this month following a tense transfer stand off with Newcastle United after the 2026 FIFA World Cup.
Guimaraes joins a packed list of options in Arteta's central midfield alongside captain Odegaard, Declan Rice, Martin Zubimendi, Mikel Merino and Myles Lewis-Skelly.
Zubimendi has been linked with a move away to Real Madrid, if his starting role is taken away, and Odegaard was impressed by Guimaraes' competitive debut in Arsenal's 3-0 FA Community Shield win over rivals Manchester City.
"It's been so natural, I think the connection is already there.
"You can see he's a top, top player from the first second he's in training, you feel that presence and quality. It's been really easy to connect with him, he's a brilliant player.
"Since the first day, it's been natural. Although we had some big fights in the past with him, he's just come in as a really natural part of the team, and you can see his quality.
"He can win the ball, he's a fighter, but also has so much quality on the ball."
Guimaraes was replaced at half-time by Rice, with Zubimendi given the final 15 minutes, and the race is on to secure a starting spot for the Premier League campaign opener at home to Coventry City on August 21st.