The 760 marked a new strategy for Volvo, as they introduced the executive six-cylinder model first with the four-cylinder 740 only following a few years later. Jan Wilsgaard, head of Volvo's Design and Styling Team, proposed over 50 new designs for the new car. Unusual for a new executive car at the time, the 760 had a live rear axle – Volvo's designers claimed that a well-designed one was at least as capable as any independent design, while offering substantial cost and weight savings. The axle itself was mounted almost entirely behind the passenger compartment, freeing up more space inside, and was unusual in that it is mounted in a sub-frame, allowing better passenger comfort than a conventional setup. Volvo called the system Constant Track Rear Suspension, drawing attention to another benefit of a live axle.

It was introduced to the U.S. in 1982 for the 1983 model year as the 760 GLE saloon, with the V6 engine coupled to an automatic transmission, having been launched in Sweden in February 1982 and in Britain from July 1982.The federalized Turbo Diesel went on sale a few months later, at the very end of 1982. In February 1985 the 760 Station Wagon ("765" in internal parlance) was introduced, going on sale in US and Canada a few months later. European markets only received the wagons beginning in the autumn, for the 1986 model year.