A complete set of pseudopotentials and accompanying basis sets for all lanthanide elements are presented based on the relativistic, norm-conserving, separable, dual-space Gaussian-type pseudopotential protocol of Goedecker, Teter, and Hutter (GTH) within the generalized gradient approximation (GGA) and the exchange-correlation functional of Perdew, Burke, and Ernzerhof (PBE). The corresponding basis sets have been molecularly optimized (MOLOPT) using a contracted form with a single set of Gaussian exponents for the s, p, and d states. The f states are uncontracted explicitly with Gaussian exponents. Moreover, the Hubbard U values for each lanthanide element, for DFT+U calculations, are also tabulated, allowing for the proper treatment of the strong on-site Coulomb interactions of localized 4f electrons. The accuracy and reliability of our GTH pseudopotentials and companion basis sets optimized for lanthanides is illustrated by a series of test calculations on lanthanide-centered molecules, and solid-state systems, with the most common oxidation states. We anticipate that these pseudopotentials and basis sets will enable larger-scale density functional theory calculations and ab initio molecular dynamics simulations of lanthanide molecules in either gas or condensed phases, as well as of solid state lanthanide-containing materials, allowing further exploration of the chemical and physical properties of lanthanide systems.