We present an analysis of the X-ray point source populations in 182 Chandra images of galaxy clusters at z>0.1 with exposure time >10 ksec, as well as 44 non-cluster fields. Analysis of the number and flux of these sources, using a detailed pipeline to predict the distribution of non-cluster sources in each field, reveals an excess of X-ray point sources associated with the galaxy clusters. A sample of 148 galaxy clusters at 0.1<z<0.9, with no other nearby clusters, show an excess of 230 cluster sources in total, an average of ~1.5 sources per cluster. The lack of optical data for these clusters limits the physical interpretation of this result, as we cannot calculate the fraction of cluster galaxies hosting X-ray sources. However, the fluxes of the excess sources indicate that over half of them are very likely to be AGN, and the radial distribution shows that they are quite evenly distributed over the central 1 Mpc of the cluster, with almost no sources found beyond this radius. We also use this pipeline to successfully reproduce the results of previous studies, particularly the higher density of sources in the central 0.5 Mpc of a few cluster fields, but show that these conclusions are not generally valid for this larger sample of clusters. We conclude that some of these differences may be due to the sample properties, such as the size and redshift of the clusters studied, or a lack of publications for cluster fields with no excess sources. This paper also presents the basic X-ray properties of the galaxy clusters, and in subsequent papers in this series the dependence of the AGN population on these cluster properties will be evaluated. In addition the properties of over 9500 X-ray point sources in the fields of galaxy clusters are tabulated in a separate catalogue available online.
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