With the completion of the ALMA array, Development Projects are being initiated to expand the observatory's technical capabilities. The ALMA Phasing Project is one of the early ones, with the main goal of adding Very Long Baseline Interferometry (VLBI) observation capabilities. This will enable ALMA to join observations with other millimeter observatories having VLBI data capabilities around the globe. ALMA would therefore become the most powerful millimeter VLBI station yet.A minimal impact approach has been taken to cause as little overall work overhead at the observatory as possible and integrate seamlessly with existing infrastructure. New hardware elements and software features are being delivered in incremental cycles to the observatory, adhering to existing workflows.This paper addresses one of the main software challenges of this project and its implementation: the continuous phasing corrections of the ALMA antenna signals. As antenna signals are summed during the online processing for correlation after the observation, a phased array is a key requirement for successful VLBI observations. A new observing mode that inherits all of the existing interferometry functionality is the cornerstone of this development. Further additions include new correlator protocols to modify the data flow, new VLBI specific device controllers, online phase solvers and observation metadata adaptations. All of these are being added to existing ALMA Software subsystems, taking advantage of the modular design and reusing as much code as possible.The design has included a strong focus on simulation capabilities to verify as much of the functionality as possible without the need for sparse telescope time. The first on-site tests of the phasing loop using the ALMA baseline correlator and antennas were performed in early 2014, and the hardware is expected to be completely installed by the middle of the same year.