He joins the Hornets for a fee reported to be close to £3m on a three-year deal, keeping him at the club until 2025.
Kalu arrives at Vicarage Road after three and a half years with Ligue 1 side Bordeaux, where he scored nine goals in 86 appearances.
The 24-year-old has 17 caps for Nigeria and has scored twice for the Super Eagles.
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