Hodge, 42, held a similar role with Gujarat Lions for the last two seasons and will now report to KXIP's mentor-cum director of cricket, Virender Sehwag.
KXIP's head coach's job was informally held by Sehwag after India team's batting coach Sanjay Bangar resigned in December 2016.
"We have signed a three-year agreement with Brad, who will be our head coach," Kings XI Punjab co-owner Ness Wadia was quoted as saying by ESPNcricinfo.
"Viru (Sehwag) will be actively involved, too, as our director of cricket."
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