The magnetic configuration hosting prominences and their surrounding coronal
structure is a key research topic in solar physics. Recent theoretical and
observational studies strongly suggest that a helical magnetic flux rope is a
key ingredient to fulfill most of the theoretical and observational requirements
 for hosting prominences. The formation of a flux rope has to date been studied
by models based on force-free extrapolations or zero-beta magnetohydrodynamic
simulations. The key process, involving magnetic reconnection of sheared
magnetic arcades at polarity inversion lines, has not fully been demonstrated.
To understand flux rope formation details and obtain magnetic configurations
suitable for future prominence formation studies, we here report on
three-dimensional isothermal magnetohydrodynamic simulations including finite
gas pressure and gravity. Starting from a magnetohydrostatic corona with a
linear force-free bipolar magnetic field, we follow its evolution when
introducing vortex flows around the main polarities and converging flows
 towards the polarity inversion near the bottom of the corona. The converging
flows bring feet of different loops together above the polarity inversion line
and magnetic reconnection happens. Outflow signatures of the reconnection
process are identified, and the thereby newly formed helical loops wind around
pre-existing ones so that a complete flux rope grows and ascends. When a
macroscopic flux rope is formed, we switch off the driving flows and find that
the system relaxes to a stable state containing a helical magnetic flux rope
embedded in an overlying arcade structure. This is the first numerical
demonstration of large-scale stable helical flux rope formation which includes
plasma and gravitational stratification effects. This paves the way to true
ab-initio simulations for prominence-hosting magnetic configurations.