Jim Caviezel stars alongside Lost's Michael Emerson in the action drama, currently airing its second season on CBS.
Brown - who has appeared on Supernatural, Third Watch and Army Wives - will play a narcotics detective, Deadline reports.
His character Cal Beecher is being envisioned as a potential love interest for Detective Carter, played by Taraji P Henson.
Earlier this month, it was revealed that Lost and Supernatural actor Mark Pellegrino had also been cast on Person of Interest - the star will play the head of a publishing empire in a future episode.
Taraji P Henson previously told Digital Spy that she is eager to explore more of her character Carter's personal life.
"I feel like there are layers of all the characters to be revealed, but Carter especially," she said. "It's all done very slowly and cleverly. The writers keep the audience wanting more."
Person of Interest continues on Thursday nights in the US and airs on Channel 5 in the UK.
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Watch a clip from Person of Interest below: