Matthews told reporters that he chose to sign the Pacers because he's been assured a starting job with the team.
"That's how I view myself, and that's how this organization views me. That's big right there," he said, according to the Indianapolis Star.
The move was first reported following Thursday's trade deadline, but the Pacers couldn't announce it until Sunday. Matthews was waived by the Knicks after a deal that sent Kristaps Porzingis to Dallas. He cleared waivers Saturday.
Terms of the deal were not announced.
Matthews, 32, will help fill the void left by All-Star guard Victor Oladipo, who will miss the rest of this season with a ruptured quad tendon in his right knee.
Pacers coach Nate McMillan confirmed that Matthews will start.
"He didn't come here to sit on the bench," McMillan told reporters, according to the Star. "That was part of it, being a starter. We felt we could bring him in as a starter."
McMillan has coached Matthews before with the Portland Trail Blazers.
In 44 games with Dallas, Matthews made 44 starts and averaged 13.1 points, 2.3 rebounds and 2.3 assists.
Pacers president of basketball operations Kevin Pritchard called Matthews a "solid professional" who will "fit in well" with Indiana.
The Associated Press contributed to this report.