Context: The source 4U 2206+54 is one of the most enigmatic high-mass X-ray binaries. In spite of intensive searches, X-ray pulsations have not been detected in the time range 10-3-103 s. A cyclotron line at ~30 keV has been suggested by various authors but never detected with significance. The stellar wind of the optical companion is abnormally slow. The orbital period, initially reported to be 9.6 days, disappeared and a new periodicity of 19.25 days emerged. Aims: The main objective of our RXTE monitoring of 4U 2206+54 is to study the X-ray orbital variability of the spectral and timing parameters. The new long and uninterrupted RXTE observations allow us to search for long (~1 h) pulsations for the first time. Methods: We divided the ~7-day observation into five intervals and obtained time-averaged energy spectra and power spectral density for each observation interval. We also searched for pulsations using various algorithms. Results: We have discovered 5560-s pulsations in the light curve of 4U 2206+54. Initially detected in RXTE data, these pulsations are also present in INTEGRAL and EXOSAT observations. The average X-ray luminosity in the energy range 2-10 keV is 1.5 × 1035 erg s-1 with a ratio F_max/F_min ≈ 5. This ratio implies an eccentricity of ~0.4, somewhat higher than previously suggested. The power spectrum is dominated by red noise that can be fitted with a single power law whose index and strength decrease with X-ray flux. The source also shows a soft excess at low energies. If the soft excess is modelled with a blackbody component, then the size and temperature of the emitting region agrees with its interpretation in terms of a hot spot on the neutron star surface. Conclusions: The discovery of X-ray pulsations in 4U 2206+54 confirms the neutron star nature of the compact companion and definitively rules out the presence of a black hole. The source displays variability on time scales of days, presumably due to changes in the mass accretion rate as the neutron star moves around the optical companion in a moderately eccentric orbit. If current models for the spin evolution in X-ray pulsars are correct, then the magnetic field of 4U 2206+54 at birth must have been B ≳ 1014 G.