Tens of millions of new variable objects are expected to be identified in over a billion time series from the Gaia mission. Crossmatching known variable sources with those from Gaia is crucial to incorporate current knowledge, understand how these objects appear in the Gaia data, train supervised classifiers to recognise known classes, and validate the results of the Variability Processing and Analysis Coordination Unit (CU7) within the Gaia Data Analysis and Processing Consortium (DPAC). The method employed by CU7 to crossmatch variables for the first Gaia data release includes a binary classifier to take into account positional uncertainties, proper motion, targeted variability signals, and artefacts present in the early calibration of the Gaia data. Crossmatching with a classifier makes it possible to automate all those decisions which are typically made during visual inspection. The classifier can be trained with objects characterized by a variety of attributes to ensure similarity in multiple dimensions (astrometry, photometry, time-series features), with no need for a-priori transformations to compare different photometric bands, or of predictive models of the motion of objects to compare positions. Other advantages as well as some disadvantages of the method are discussed. Implementation steps from the training to the assessment of the crossmatch classifier and selection of results are described.