Aims: We aim to characterize the broadband emission from 2FGL J2001.1+4352, which has been associated with the unknown-redshift blazar MG4 J200112+4352. Based on its gamma-ray spectral properties, it was identified as a potential very high energy (VHE; E> 100 GeV) gamma-ray emitter. We investigate whether this object is aVHE emitter, characterize its gamma-ray spectrum, and study the broadband emission within the one-zone synchrotron self-Compton (SSC) scenario, which is commonly used to describe the emission in blazars. Moreover, we also intend to determine the redshift of this object, which is a crucial parameter for its scientific interpretation. Methods: The source was observed with MAGIC first in 2009 and later in 2010 within a multi-instrument observation campaign. The MAGIC observations yielded 14.8 h of good quality stereoscopic data. Besides MAGIC, the campaign involved, observations with Fermi-LAT, Swift-XRT/UVOT, the optical telescopes KVA, Goddard Robotic Telescope, Galaxy View observatory, Crimean Astrophysical observatory, St. Petersburg observatory, and the Owens Valley Radio Observatory. The object was monitored at radio, optical and gamma-ray energies during the years 2010 and 2011. We characterize the radio to VHE spectral energy distribution and quantify the multiband variability and correlations over short (few days) and long (many months) timescales. We also organized deep imaging optical observations with the Nordic Optical Telescope in 2013 to determine the source redshift. Results: The source, named MAGIC J2001+439, is detected for the first time at VHE with MAGIC at a statistical significance of 6.3σ (E > 70 GeV) during a 1.3 h long observation on 2010 July 16. The multi-instrument observations show variability in all energy bands with the highest amplitude of variability in the X-ray and VHE bands. Besides the variability on few-day timescales, the long-term monitoring of MAGIC J2001+439 shows that, the gamma-ray, optical, and radio emissions gradually decreased on few-month timescales from 2010 through 2011, indicating that at least some of the radio, optical and gamma-ray emission is produced in a single region by the same population of particles. We also determine for the first time the redshift of this BL Lac object through the measurement of its host galaxy during low blazar activity. Using the observational evidence that the luminosities of BL Lac host galaxies are confined to a relatively narrow range, we obtain z = 0.18 ± 0.04. Additionally, we use the Fermi-LAT and MAGIC gamma-ray spectra to provide an independent redshift estimation, z = 0.17 ± 0.10. Using the former (more accurate) redshift value, we adequately describe the broadband emission with a one-zone SSC model for different activity states and interpret the few-day timescale variability as produced by changes in the high-energy component of the electron energy distribution. Appendix A is available in electronic form at http://www.aanda.org