Earthquake early warning systems are required to report earthquake locations and magnitudes as quickly as possible before the damaging S wave arrival to mitigate seismic hazards. Deep learning techniques provide potential for extracting earthquake source information from full seismic waveforms instead of seismic phase picks. We developed a novel deep learning earthquake early warning system that utilizes fully convolutional networks to simultaneously detect earthquakes and estimate their source parameters from continuous seismic waveform streams. The system determines earthquake location and magnitude as soon as one station receives earthquake signals and evolutionarily improves the solutions by receiving continuous data. We apply the system to the 2016 Mw 6.0 earthquake in Central Apennines, Italy and its subsequent sequence. Earthquake locations and magnitudes can be reliably determined as early as four seconds after the earliest P phase, with mean error ranges of 6.8-3.7 km and 0.31-0.23, respectively.