Context. After more than two decades of relevant radial velocity surveys, the current sample of known brown dwarfs (BDs) around FGK-stars is only of the order of a hundred, limiting our understanding of their occurrence rate, properties, and formation. The ongoing ESA mission Gaia has already collected more than its nominal 5 years of mission data, and is expected to operate for up to 10 years in total. Its exquisite astrometric precision allows for the detection of (unseen) companions down to the Jupiter-mass level, hence allowing for the efficient detection of large numbers of brown dwarfs. Additionally, its low-accuracy multi-epoch radial velocity measurements for G RVS < 12 can provide additional detections or constraints for the more massive BDs, while a further small sample will have detectable transits in the Gaia photometry. Aims. Using detailed simulations, we provide an assessment of the number of brown dwarfs that could be discovered by Gaia astrometry, radial velocity, and photometric transits around main sequence (V) and subgiants (IV) FGK host stars for the nominal 5-yr and extended 10-yr mission. Methods. Using a robust ∆χ 2 statistic we analyse the BD companion detectability from the Besançon Galaxy population synthesis model for G = 10.5 − 17.5 mag, complemented by Gaia DR2 data for G < 10.5, using the latest Gaia performance and scanning law, and literature-based BD-parameter distributions. Results. We report here only reliable detection numbers with ∆χ 2 > 50 for a 5-year mission and between square brackets for a 10-year mission. For astrometry alone we expect 28 000-42 000 [45 000-55 000] detections out to several hundred pc [up to more than a kiloparsec]. The majority of these have G ∼ 14 − 15 [14 − 16] and periods above 200 d, extending up to the longest simulated periods of 5 year. Gaia radial velocity time series for G RVS < 12 (G 12.7), should allow the detection of 830-1100 [1500-1900] BDs, most having orbital periods <10 days, and being amongst the most massive BDs (55 − 80M J ), though several tens will extend down to the 'desert' and lowest BD masses. Systems with at least three photometric transits having S/N>3 are expected for 720-1100 [1400-2300] BDs, averaging at 4-5 [5-6] transits per source. The combination of astrometric and radial velocity detections should yield some 370-410 [870-950] detections. BDs have both transit and radial velocity detections, while both transits and astrometric detection will lead to a meagre 1-3 [4-6] detection(s). Conclusions. Though above numbers have ±50% uncertainty due to the uncertain occurrence rate and period distribution of BDs around FGK host stars, detections of BDs with Gaia will number in the tens-of-thousands, enlarging the current BD sample by at least two orders of magnitude and thus allowing to investigate the BD fraction and orbital architectures as a function of host stellar parameters in greater detail than every before.