Laser-induced electron recollisions are fundamental to many strong field phenomena in atoms and molecules. Using the recently developed quantitative rescattering theory, we demonstrate that the nonsequential double ionization NSDI of atoms by lasers can be obtained quantitatively in terms of inelastic collisions of the target ions with the free returning electrons where the latter are explicitly given by a spectrum-characterized wave packet. Using argon atoms as target, we calculated the NSDI yield including contributions from direct e,2e electron-impact ionization and electron-impact excitation accompanied by subsequent field ionization. We further investigate the dependence of total NSDI on the carrier-envelope phase of few-cycle laser pulses, and showed that the effect can be experimentally observed by measuring the yield of doubly charged ions only.