Our Solar System moves through a warm (~6,500 K), partly ionized local interstellar cloud (LIC) with a relative speed of ~26 km/s. The solar wind interacts with the LIC to form a cavity around the Sun called the heliosphere. The solar wind meets the interstellar charged component at the heliopause, where solar wind pressure balances the pressure of the LIC. Before reaching the heliopause, the supersonic solar wind is decelerated at an extended shock wave, the heliospheric termination shock (TS). The two Voyager spacecraft are cruising away from the Sun and approaching the termination shock. Here we present predictions of when the Voyagers will encounter the termination shock by calculating the position of the TS using a numerical multi-component model of the heliospheric interface and improved measurements of interstellar H atoms. Interstellar atoms penetrate into the heliosphere where they are ionized and detected as pickup ions by the SWICS instrument on Ulysses. We conclude that the most probable crossing of the termination shock by Voyager 1 will occur between 2007 and 2012.