We present redshift evolution of galaxy effective radius r e obtained from the Hubble Space Telescope (HST) samples of ∼ 190, 000 galaxies at z = 0 − 10. Our HST samples consist of 176, 152 photo-z galaxies at z = 0 − 6 from the 3D-HST+CANDELS catalogue and 10, 454 Lyman break galaxies (LBGs) at z = 4 − 10 identified in CANDELS, HUDF09/12, and HFF parallel fields, providing the largest data set to date for galaxy size evolution studies. We derive r e with the same technique over the wide-redshift range of z = 0 − 10, evaluating the optical-to-UV morphological K-correction and the selection bias of photo-z galaxies+LBGs as well as the cosmological surface brightness dimming effect. We find that r e values at a given luminosity significantly decrease towards high-z, regardless of statistics choices (e.g. r e ∝ (1 + z) −1.10±0.06 for median). For star-forming galaxies, there is no evolution of the power-law slope of the size-luminosity relation and the median Sérsic index (n ∼ 1.5). Moreover, the r e -distribution is well represented by log-normal functions whose standard deviation σ ln re does not show significant evolution within the range of σ ln re ∼ 0.45 − 0.75. We calculate the stellar-to-halo size ratio from our r e measurements and the dark-matter halo masses estimated from the abundance matching study, and obtain a nearly constant value of r e /r vir = 1.0 − 3.5% at z = 0 − 8. The combination of the r e -distribution shape+standard deviation, the constant r e /r vir , and n ∼ 1.5 suggests a picture that typical high-z star-forming galaxies have disk-like stellar components in a sense of dynamics and morphology over cosmic time of z ∼ 0 − 6. If high-z star-forming galaxies are truly dominated by disks, the r e /r vir value and the disk formation model indicate that the specific angular momentum of the disk normalized by the host halo is j d /m d ≃ 0.5 − 1. These are statistical results for galaxies' major stellar components, and the detailed study of clumpy sub-components is presented in the paper II.