The H{alpha} nebular emission line is an optimal tracer for recent star formation in galaxies. With the advent of JWST, this line has recently become observable at z>3 for the first time. We present a catalog of 1050 H{alpha} emitters at 3.7<z<6.7 in the GOODS fields obtained from a blind search in JWST NIRCam/grism data. We made use of the FRESCO survey's 124 arcmin^2^ of observations in GOODS-North and GOODS-South with the F444W filter, probing H{alpha} at 4.9<z<6.7, and the CONGRESS survey's 62 arcmin^2^ of observations in GOODS-North with F356W, probing H{alpha} at 3.8<z<5.1. We found an overdensity with 98 sources at z~4.4 in GOODS-N, and confirmed previously reported overdensities at z~5.2 in GOODS-N and at z~5.4 and z~5.9 in GOODS-S. We computed the observed H{alpha} luminosity functions (LFs) in three bins centered at z~4.45, 5.30, and 6.15, which are the first such measurements at z>3 obtained based purely on spectroscopic data, robustly tracing galaxy star formation rates (SFRs) beyond the peak of the cosmic star formation history. We compared our results with theoretical predictions from three different simulations and found good agreement at z~4-6. The UV LFs of this spectroscopically confirmed sample are in good agreement with pre-JWST measurements obtained with photometrically selected objects. Finally, we derived SFR functions and integrated them to compute the evolution of the cosmic SFR densities across z~4-6, finding values in good agreement with recent UV estimates from Lyman-break galaxies, which imply a continuous decrease in SFR density by a factor of three over z~4 to z~6. Our work shows the power of NIRCam grism observations to efficiently provide new tests for early galaxy formation models based on emission line statistics.