The open solar magnetic flux has been recently reconstructed by Solanki et al. <2000, 2002> for the last 400 years from sunspot data. Using this reconstructed magnetic flux as an input to a spherically symmetric quasi-steady state model of the heliosphere, we calculate the expected intensity of galactic cosmic rays at the Earth's orbit since 1610. This new, physical reconstruction of the long-term cosmic ray intensity is in good agreement with the neutron monitor measurements during the last 50 years. Moreover, it resolves the problems related to previous reconstruction for the last 140 years based on linear correlations. We also calculate the flux of 2 GeV galactic protons and compare it to the cosmogenic 10Be level in polar ice in Greenland and Antarctica. An excellent agreement between the calculated and measured levels is found over the last 400 years.