Nearly every massive galaxy harbors a supermassive black hole (SMBH) in its nucleus. SMBH masses are millions to billions of solar mass, and they correlate with properties of spheroids of their host galaxies. While the SMBH growth channels, mergers, and gas accretion are well established, their origin remains uncertain: they could have emerged either from massive "seeds" (10(5)-10(6)M(circle dot)) formed by direct collapse of gas clouds in the early universe or from smaller (100M(circle dot)) BHs, end products of first stars. The latter channel would leave behind numerous intermediate-mass BHs (IMBHs, 10(2)-10(5) M-circle dot). Although many IMBH candidates have been identified, none are accepted as definitive; thus, their very existence is still debated. Using data mining in wide-field sky surveys and applying dedicated analysis to archival and follow-up optical spectra, we identified a sample of 305 IMBH candidates having masses 3 x 10(4) M-e < M-BH < 2 x 10(5) M-circle dot, which reside in galaxy centers and are accreting gas that creates characteristic signatures of a type I active galactic nucleus (AGN). We confirmed the AGN nature of 10 sources (including five previously known objects that validate our method) by detecting the X-ray emission from their accretion disks, thus defining the first bona fide sample of IMBHs in galactic nuclei. All IMBH host galaxies possess small bulges and sit on the low-mass extension of the M-BH-M-bulge scaling relation, suggesting that they must have experienced very few if any major mergers over their lifetime. The very existence of nuclear IMBHs supports the stellar-mass seed scenario of the massive BH formation.