Although the Gaia catalogue on its own will be a very powerful tool, it is the combination of this highly accurate archive with other archives that will truly open up amazing possibilities for astronomical research. The advanced interoperation of archives is based on cross-matching, leaving the user with the feeling of working with one single data archive. The data retrieval should work not only across data archives, but also across wavelength domains. The first step for seamless data access is the computation of the cross-match between Gaia and external surveys. The matching of astronomical catalogues is a complex and challenging problem both scientifically and technologically (especially when matching large surveys like Gaia). We describe the cross-match algorithm used to pre-compute the match of Gaia Data Release 1 (DR1) with a selected list of large publicly available optical and IR surveys. The overall principles of the adopted cross-match algorithm are outlined. Details are given on the developed algorithm, including the methods used to account for position errors, proper motions, and environment; to define the neighbours; and to define the figure of merit used to select the most probable counterpart. Statistics on the results are also given. The results of the cross-match are part of the official Gaia DR1 catalogue.