In immunocompromised individuals, JC polyomavirus (JCPyV) may mutate and gain access to the central nervous system resulting in progressive multifocal leukoencephalopathy (PML), an often fatal opportunistic infection for which no treatments are currently available. Despite recent progress, the contribution of JCPyV-specific humoral immunity to controlling asymptomatic infection throughout life and to eliminating JCPyV from the brain is poorly understood. We examined antibody responses against JCPyV major capsid protein VP1 (viral protein 1) variants in the serum and cerebrospinal fluid (CSF) of healthy donors (HDs), JCPyV-positive multiple sclerosis patients treated with the anti-VLA-4 monoclonal antibody natalizumab (NAT), and patients with NAT-associated PML. Before and during PML, CSF antibody responses against JCPyV VP1 variants show “recognition holes”; however, upon immune reconstitution, CSF antibody titers rise, then recognize PML-associated JCPyV VP1 variants, and may be involved in elimination of the virus. We therefore reasoned that the memory B cell repertoire of individuals who recovered from PML could be a source for the molecular cloning of broadly neutralizing antibodies for passive immunization. We generated a series of memory B cell-derived JCPyV VP1-specific human monoclonal antibodies from HDs and a patient with NAT-associated PML-immune reconstitution inflammatory syndrome (IRIS). These antibodies exhibited diverse binding affinity, cross-reactivity with the closely related BK polyomavirus, recognition of PML-causing VP1 variants, and JCPyV neutralization. Almost all antibodies with exquisite specificity for JCPyV, neutralizing activity, recognition of all tested JCPyV PML variants, and high affinity were derived from one patient who had recovered from PML. These antibodies are promising drug candidates for the development of a treatment of PML.