We present the observation of doubly produced J/ψ mesons with the D0 detector at Fermilab in pp¯ collisions at s√=1.96  TeV. The production cross section for both singly and doubly produced J/ψ mesons is measured using a sample with an integrated luminosity of 8.1  fb−1. For the first time, the double J/ψ production cross section is separated into contributions due to single and double parton scatterings. Using these measurements, we determine the effective cross section σeff, a parameter characterizing an effective spatial area of the parton-parton interactions and related to the parton spatial density inside the nucleon.