The 760 was Volvo's attempt to cement a place in the prestige market, after building a reputation for being solid and safe rather than out-and-out luxurious cars. Jan Wilsgaard, head of Volvo's Design and Styling team, proposed over 50 new designs for the new car. It was introduced to the US in 1982 for the 1983 model year as the 760 GLE sedan. This new design was criticized by the media when released: Gordon Murray of Autocar Magazine said, "To me it's obscene! That goes right against the grain of what everybody else is trying to do. To me it looks like a European version of a North American car. It produces the same amount of power as a 2600 or 3500 — in this day and age it disgusts me to see something about like that. It's a definite step backwards." All that changed however when Autocar and Car & Driver got their hands on a turbo intercooled 760; they said it was one of the best handling and fastest accelerating cars they had seen in a while, thundering from 0-60 mph (97 km/h) in under 8 seconds.
Turbocharged and intercooled variants were added in 1984, station wagon variants and the 740 – the 760's lower-specification sibling – were introduced for the 1985 model year. In 1985 Electronic Traction Control system was introduced. For the 1988 model year, the 760 received numerous updates. From the outside, the most noticeable of the over 2,000 changes were the revised front sheetmetal, including an aluminium hood, recessed windscreen wipers, and new aerodynamic headlights. Inside, all 760s were equipped with a new electronic climate control (ECC), a revised dashboard, three-position tilt steering, and a new stereo system. Underneath, sedans received the same multi-link independent rear suspension that was used on the 780. Along with the revised dash, the interior saw the addition of a revised dome light and many fabric accent pieces.
The Volvo 760 was also used as a police car in several countries. East German dictator Erich Honecker also often used this Volvo in his governmental car pool.