The continuous growth of geophysical observations requires adequate methods for their processing and analysis. This becomes one of the most important and widely discussed issues in the data science community. The system analysis methods and data mining techniques are able to sustain the solution of this problem. This paper presents an innovative holistic hardware/software system (HSS) developed for efficient management and intellectual analysis of geomagnetic data, registered by Russian geomagnetic observatories and international satellites. Geomagnetic observatories that comprise the International Real-time Magnetic Observatory Network (INTERMAGNET) produce preliminary (raw) and definitive (corrected) geomagnetic data of the highest quality. The designed system automates and accelerates routine production of definitive data from the preliminary magnetograms, obtained by Russian observatories, due to implemented algorithms that involve artificial intelligence elements. The HSS is the first system that provides sophisticated automatic detection and multi-criteria classification of extreme geomagnetic conditions, which may be hazardous for technological infrastructure and economic activity in Russia. It enables the online access to digital geomagnetic data, its processing results and modelling calculations along with their visualization on conventional and spherical screens. The concept of the presented system agrees with the accepted 'four Vs' paradigm of Big Data. The HSS can increase significantly the 'velocity' and 'veracity' features of the INTERMAGNET system. It also provides fusion of large sets of ground-based and satellite geomagnetic data, thus facilitating the 'volume' and 'variety' of handled data.