Infant and childhood growth are dynamic processes with large changes in BMI during development. By performing genome-wide association studies of BMI at 12 time points from birth to eight years (9286 children, 74,105 measurements) in the Norwegian Mother, Father, and Child Cohort Study, replicated in 5235 children, we identify a transient effect in the leptin receptor (LEPR) locus: no effect at birth, increasing effect in infancy, peaking at 6-12 months (rs2767486, P6m = 2.0 × 10-21, β6m = 0.16 sd-BMI), and little effect after age five. We identify a similar transient effect near the leptin gene (LEP), peaking at 1.5 years (rs10487505, P1.5y = 1.3 × 10-8, β1.5y = 0.079 sd-BMI). Both signals are protein quantitative trait loci for soluble-LEPR and LEP in plasma in adults independent from adult traits mapped to the respective genes, suggesting key roles of common variation in the leptin signaling pathway for healthy infant growth.