Gaia16aye was a binary microlensing event discovered in the direction towards the northern Galactic disc and was one of the first microlensing events detected and alerted to by the Gaia space mission . Its light curve exhibited five distinct brightening episodes , reaching up to I=12 mag , and it was covered in great detail with almost 25,000 data points gathered by a network of telescopes . We present the photometric and spectroscopic follow-up covering 500 days of the event evolution . We employed a full Keplerian binary orbit microlensing model combined with the motion of Earth and Gaia around the Sun to reproduce the complex light curve . The photometric data allowed us to solve the microlensing event entirely and to derive the complete and unique set of orbital parameters of the binary lensing system . We also report on the detection of the first-ever microlensing space-parallax between the Earth and Gaia located at L2 . The properties of the binary system were derived from microlensing parameters , and we found that the system is composed of two main-sequence stars with masses 0.57 \pm 0.05 M _ { \mathrm { \odot } } and 0.36 \pm 0.03 M _ { \mathrm { \odot } } at 780 pc , with an orbital period of 2.88 years and an eccentricity of 0.30 . We also predict the astrometric microlensing signal for this binary lens as it will be seen by Gaia as well as the radial velocity curve for the binary system . Events such as Gaia16aye indicate the potential for the microlensing method of probing the mass function of dark objects , including black holes , in directions other than that of the Galactic bulge . This case also emphasises the importance of long-term time-domain coordinated observations that can be made with a network of heterogeneous telescopes .