Rhodes' deal is worth around $5 million, according to Tom Pelissero of NFL Network.
The 29-year-old is coming off a seven-year stint with the Vikings. He was cut before free agency opened in a move that saved Minnesota over $8 million against the salary cap.
Rhodes made three Pro Bowls with the Vikings and was named a first-team All-Pro in 2017, but struggled over the last two years. He didn't record an interception in 2019 for the first time since his rookie year.
The Colts added the veteran to their secondary just days after releasing Pierre Desir, who had been their top cornerback.
In 15 games last season, Rhodes had 63 tackles and broke up six passes.