The New Zealand-born striker is currently on loan with Millwall but will join the Foxes permanently when that temporary deal expires.
The 21-year-old has scored 11 goals in 19 appearances in the English second tier this term, and is believed to cost Leicester up to £2 million.
Dan Ashworth, the Baggies' sporting & technical director, told the club's official website: “Chris joined our Academy as a 15-year-old and has progressed through the ranks.
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“He’s now had two or three really good spells out on loan and this is a good time for him to begin a new, permanent challenge.
“Chris is a great lad and we’re particularly grateful for his contribution to our automatic promotion success of four seasons ago.
“We wish him all the best at Leicester.”
Wood made just 21 appearances for West Brom in total, with 18 of those coming in a successful 2009-10 promotion push.
He has since enjoyed loan spells with Barnsley, Brighton, Birmingham and Bristol City.