Nagra played Lucy Banerjee on the sci-fi drama, which was recently axed by Fox.
The actress has now been cast as Rachel, a love interest for Gus (Dule Hill) on USA's Psych, reports TVLine.
The comedy-drama - which also stars James Roday - is currently filming its seventh season.
Nagra is known for starring in 2002 film Bend It Like Beckham and for her series regular role on ER from 2003 to 2009.
Psych will return to USA with 16 new episodes in late 2012.
> 'Psych' picked up for seventh season by USA Network
> The 2012-13 season TV scorecard: What's axed? What's renewed?
Watch a promo for the new season of Psych below: