We reconstruct the history of the cosmic star formation in the universe by means of detailed chemical evolution models for galaxies of different morphological types. We consider a picture of coeval, non-interacting evolving galaxies where ellipticals experience intense and rapid starbursts within the first Gyr after their formation, and spirals and irregulars continue to form stars at lower rates up to the present time. Such models allow one to follow in detail the evolution of the metallicity of the gas out of which the stars are formed. We normalize the galaxy population to the B band luminosity function observed in the local Universe and study the redshift evolution of the luminosity densities in the B, U, I and K bands calculating galaxy colors and evolutionary corrections by means of a detailed synthetic stellar population model. Our predictions indicate that the decline of the galaxy luminosity density between redshift 1 and 0 observed in the U, B and I bands is caused mainly by star-forming spiral galaxies which slowly exhaust their gas reservoirs. Elliptical galaxies have dominated the total luminosity density in all optical bands at early epochs, when all their stars formed by means of rapid and very intense star-bursts. Irregular galaxies bring a negligible contribution to the total luminosity density in any band at any time. (abridged)