The 23-year-old sits atop the Rookie of the Year standings despite running a partial campaign that has consisted solely of road and street circuits. He has recorded three top-eight results in 11 IndyCar starts.
A former member of Ferrari's Driver Academy, Armstrong arrived in IndyCar after three years in Formula 2, winning four races and scoring a further four podiums from 2020-22.
His first taste of an oval will be at a test at Texas Motor Speedway on 13 September.
"I am very proud and excited to continue with Chip Ganassi Racing for next year and beyond," Armstrong said.
"Together with this very talented and experienced team, I am confident we can compete at the highest level in this championship. I feel very grateful that Chip has given me the time to adapt to IndyCar and has helped me every step of the way in what has been a good season.
"I've spent the year learning from a great group of people, including my team-mates and Dario [Franchitti]. I'm very grateful for how much help I've received from each team member.
"With a season under my belt, I now want to turn these lessons into results. I will be racing on the ovals for the first time next year and it's an exciting challenge that I'm confident I can learn quickly.
"I spent the entire month of May either in the engineering office or in the pit stand this year, trying to familiarize myself with the details of oval racing.
"It's a challenge that excites me a lot."
CGR managing director Mike Hull praised Armstrong's "quick adaptation to IndyCar road and street tracks" which he said had proven "he's ready to be a full-time Chip Ganassi Racing IndyCar driver".
Hull added: "Winning is integrated into his racing resume. This includes his pursuit of the 2023 IndyCar Rookie of the Year.
"He knows how to win as a team-mate. Next comes ovals at the highest global level.
"We look forward to a long-term relationship driven by growth and opportunity in the NTT IndyCar Series with Marcus."
Ganassi has signed Linus Lundqvist after his impressive cameo appearances with Meyer Shank Racing subbing for Simon Pagenaud, with fellow Swede Marcus Ericsson departing for the newly rebranded Andretti Global squad.
The four-car line-up will be completed by Scott Dixon and Alex Palou, who has U-turned from a planned switch to Arrow McLaren.
