An actively controlled rotary steerable drilling system for directional drilling of wells having a tool collar rotated by a drill string during well drilling. A bit shaft has an upper portion within the tool collar and a lower end extending from the collar and supporting a drill bit. The bit shaft is omni-directionally pivotally supported intermediate its upper and lower ends by a universal joint within the collar and is rotatably driven by the collar. To achieve controlled steering of the rotating drill bit, orientation of the bit shaft relative to the tool collar is sensed and the bit shaft is maintained geostationary and selectively axially inclined relative to the tool collar during drill string rotation by rotating it about the universal joint by an offsetting mandrel that is rotated counter to collar rotation and at the same frequency of rotation. An electric motor provides rotation to the offsetting mandrel with respect to the tool collar and is servo-controlled by signal input from position sensing elements such as magnetometers, gyroscopic sensors, and accelerometers which provide real time position signals to the motor control. In addition, when necessary, a brake is used to maintain the offsetting mandrel and the bit shaft axis geostationary. Alternatively, a turbine is connected to the offsetting mandrel to provide rotation to the offsetting mandrel with respect to the tool collar and a brake is used to servo-control the turbine by signal input from position sensors.