A search is performed for long-lived particles that decay into final states that include a pair of electrons or a pair of muons. The experimental signature is a distinctive topology consisting of a pair of charged leptons originating from a displaced secondary vertex. Events corresponding to an integrated luminosity of 19.6 (20.5) fb(-1) in the electron (muon) channel were collected with the CMS detector at the CERN LHC in proton-proton collisions at root s TeV. No significant excess is observed above standard model expectations. Upper limits on the product of the cross section and branching fraction of such a signal are presented as a function of the long-lived particle's mean proper decay length. The limits are presented in an approximately model-independent way, allowing them to be applied to a wide class of models yielding the above topology. Over much of the investigated parameter space, the limits obtained are the most stringent to date. In the specific case of a model in which a Higgs boson in the mass range 125-1000 GeV/c(2) decays into a pair of long-lived neutral bosons in the mass range 20-350 GeV= c(2), each of which can then decay to dileptons, the upper limits obtained are typically in the range 0.2-10 fb for mean proper decay lengths of the long-lived particles in the range 0.01-100 cm. In the case of the lowest Higgs mass considered (125 GeV/c(2)), the limits are in the range 2-50 fb. These limits are sensitive to Higgs boson branching fractions as low as 10(-1).