Miedecke raced his own car in open-wheel competition from the mid-1970s, finishing fourth in the 1976 Australian Formula 2 Championship in a Rennmax BN7 with sponsorship from the Sydney department store chain Grace Bros. He later campaigned a Ralt RT4-Ford in the 1982 and 1983 Australian Drivers' Championships with backing from the Port Macquarie Tourist Bureau, placing third in the championship in both years and winning Round 2 of the series on each occasion — at Adelaide International Raceway in 1982 and at Lakeside in Brisbane in 1983.
His national Grand Prix appearances with the Ralt produced strong results. At the 1981 Australian Grand Prix at Calder Park he qualified eleventh and finished fifth, one lap down on winner Roberto Moreno. He finished on the same lap as 1981 Formula One World Champion Nelson Piquet, who finished second. At the 1982 Australian Grand Prix he again qualified eleventh and finished sixth. He also won the 1981 and 1982 Malaysian Grand Prix at the Shah Alam Circuit.
Miedecke's first touring car start came at the 1986 James Hardie 1000 at Bathurst co-driving a Mercedes-Benz 190E for Bob Jane's team alongside German driver Jörg van Ommen. The car was eliminated on the first lap when van Ommen was pushed into the fence at Murray's Corner.
In 1987, businessman Don Smith formed Oxo Supercube Motorsport — later known as Miedecke Motorsport — to compete in the Australian Touring Car Championship with a pair of Ford Sierra RS Cosworths sourced from English Sierra specialist Andy Rouse. Miedecke drove the second car under the Oxo sponsorship banner. The team upgraded to the homologated Ford Sierra RS500 for the endurance races later that season, which included rounds of the inaugural World Touring Car Championship. At Bathurst, Miedecke qualified as the fastest Australian-entered Sierra after the European factory cars and ran at the front of the race during the early laps, swapping the lead with Steve Soper and Andy Rouse. His open-wheel background gave the car a handling advantage at the top of the mountain, and he was able to outbrake Soper at the end of Mountain Straight in the race's opening stages. Electrical problems and a faulty alternator eventually dropped the car to seventeenth, but the performance announced Miedecke as a serious Group A contender.
Miedecke took ownership of the team in 1988 after Smith retired. He often challenged the dominant Shell-backed Sierras of Dick Johnson and John Bowe but was consistently hampered by limited resources. At the 1988 Sandown round of the ATCC he qualified on pole — his first in touring car racing — before clutch failure ended his race before the first turn. Eggenberger Motorsport drivers Steve Soper and Pierre Dieudonné joined as co-drivers for the 1988 Bathurst 1000, but a rebuild necessitated by a qualifying crash was followed by hose failures early in the race that eventually forced retirement on lap 102.
In 1989 Miedecke gained Yokohama and Kenwood sponsorship but suffered a car fire in the ATCC at Lakeside. He and co-driver Charlie O'Brien qualified sixth for the Bathurst 1000 but were eliminated by a gearbox failure before completing a lap up the mountain. The team closed at the end of 1989.
After disbanding his own team, Miedecke joined Peter Brock's Mobil 1 Racing squad. In 2015 he returned to competition by purchasing an Aston Martin Vantage GT3, competing in the final two rounds of the Australian GT Championship in collaboration with Ross Stone. He expanded to two further Vantage GT3 cars in 2016, working with Matt Stone Racing for Australian GT and GT Asia programs. That year he and son George Miedecke won the second round of the Australian Endurance Championship at Sydney Motorsport Park.
Miedecke Motorsport returned to active competition in the inaugural GT4 Australia series in 2024. At the first round at Phillip Island, George Miedecke and co-driver Rylan Gray won a race in the Ford Mustang S650 GT4, registering what was reported as the first race victory for that model outside of North America.