We present proper motions and astrometric membership analysis for 15750 stars around the intermediate-age open cluster NGC 6819. The accuracy of relative proper motions for well-measured stars ranges from ~0.2mas/yr within 10' of the cluster center to 1.1mas/yr outside this radius. In the proper motion vector-point diagram, the separation between the cluster members and field stars is convincing down to V~18 and within 10' from the cluster center. The formal sum of membership probabilities indicates a total of ~2500 cluster members down to V~22. We confirm the cluster membership of several variable stars, including some eclipsing binaries. The estimated absolute proper motion of NGC 6819 is {mu}_x_^abs^=-2.6+/-0.5 and {mu}_y_^abs^=-4.2+/-0.5mas/yr. A cross-identification between the proper motion catalog and a list of X-ray sources in the field of NGC 6819 resulted in a number of new likely optical counterparts, including a candidate CV. For the first time we show that there is significant differential reddening toward NGC 6819.