The MAGIC Collaboration reports the detection of the blazar S5 0716+714 (z = 0.31 ± 0.08) in very high energy gamma rays. The observations were performed in 2007 November and in 2008 April, and were triggered by the Kungliga Vetenskapliga Akademi telescope due to the high optical state of the object. An overall significance of the signal accounts to S = 5.8σ for 13.1 hr of data. Most of the signal (S = 6.9σ) comes from the 2008 April data sample during a higher optical state of the object suggesting a possible correlation between the Very High Energy γ-ray and optical emissions. The differential energy spectrum of the 2008 data sample follows a power law with a photon index of Γ = 3.45 ± 0.54stat ± 0.2syst, and the integral flux above 400 GeV is at the level of (7.5 ± 2.2stat ± 2.3syst) × 10-12 cm-2 s-1, corresponding to a 9% Crab Nebula flux. Modeling of the broadband spectral energy distribution indicates that a structured jet model appears to be more promising in describing the available data than a simple one-zone synchrotron self-Compton model.