Born in 1952, Olofsson started racing in Formula Ford in 1974, finishing 2nd in the Swedish Championship. He quickly moved up to Formula Three and proved to be a very talented driver, winning his national title in 1977 with a Ralt RT1 Toyota and in 1978 as well as finishing runner up in the European championship in the same seasons. Anders was nicknamed Olof Anderson by Jan Lammers when they were driving in Formula 3.

In 1979 he only raced twice, one Formula 2 race for the Polifac BMW Junior Team with a March 792 and one round of the European F3 Championship.

He won the Special Racing Sweden series driving a Porsche in 1980 taking three wins and two other podiums in the five races. He also drove in one F3 race.

After two F2 races in 1981 he joined Volvo in 1982 for an assault on the European Touring Car Championship. Greger Pettersson brought his Volvo-Cup car to Silverstone to be driven by Olofsson and Peggen Andersson in the ETC Tourist Trophy. The car was slightly modified from Cup spec but failed to finish.

He continued to drive in the ETC until the end of 1986 when Volvo withdrew from racing. In 1986 he competed in one round of the All Japan Touring Car Championship  finishing first in the Fuji 500 driving a RAS SPORT Volvo VMS 240RXT with Johnny Cecotto.

At Le Mans in 1987 he drove the March 86G Nissan R86V with Alain Ferté and Patrick Gonin but they crashed out in the 7th hour. He also raced the March 86G Nissan R86V in the 1000 km race at Fuji finishing 13th with Takao Wada.

1988 saw another DNF at Le Mans, this time driving a March-Nissan R88S (88G-01) with Toshio Suzuki. They retired with mechanical problems after 69 laps. He also retired in the Fuji 1000Km race.

He won the Japanese Touring Car Championship in 1989 with Hasemi Motorsport driving a Nissan Skyline GTS-R with Masahiro Hasemi. He also raced a Cougar Nissan R88V for Courage Competition/Le Mans Co at Le Mans in the 24 hour race.

He raced for Nissan again in 1990. He won the Japanese Touring Car Championship again, driving with Hasemi and also drove the Nissan R90CPs in the All Japan Sports Prototype Championship, again driving with Masahiro Hasemi. The cars debuted at the 500km of Fuji and were immediately on pace, taking the second and fourth spots behind Toyota's also new 90C-V. Following the cancellation of the second round at Fuji, a third race was later held, and Nissan was able to score their first win. Hasemi and Olofsson drove their car to a two lap victory over a Porsche 962C, while the second car finished off the podium. Hoshino and Suzuki then took the next race win at the 1000km Suzuka, followed by Hasemi and Olofsson taking their second victory at Sugo. The final race of the JSPC season, once again at Fuji, saw Toyota taking victory by just over a minute. The three race wins were enough for Nissan to take the manufacturer's championship, with all four Nissan drivers tying for the drivers championship.

In 1991 he won his third consecutive Japanese Touring Car title as a works Nissan driver, once again with Hasemi, and won the 1991 Spa 24 Hour race driving a Nissan Skyline with David Brabham and Naoki Hattori.

He raced a Nissan at Bathurst in 1992. Driving with Neil Crompton they finished a fine third in the Nissan Skyline GT-R BNR32. This was the thirtieth anniversary Bathurst and was the most controversial. After a year of parity adjustments to keep BMW, Ford, Holden and Nissan even, there was already an unsettled atmosphere around the race. Peter Brock broke on the start line and Johnson took the lead. But two laps later Skaife took over and would not relinquish it. Olofsson and Neil Crompton traded second place with Johnson and John Bowe for much of the race.

Then on lap 33, Denny Hulme had a heart attack and died after his BMW drove down Con-Rod Straight only barely in control. Safety car periods prevented Skaife and Jim Richards from getting away until a storm swept across the circuit on lap 144. So many cars crashed in the suddenly downpour including Jim Richards that the race was red flagged. However the crowd, upset that a crashed car had won the race hurled abuse at the podium. Richards, already upset by the death of his friend Hulme, returned the crowds abuse. Johnson and Bowe claimed second ahead of Olofsson and Crompton, who as Nissan drivers also bore the crowds abuse, though Olofsson responded in a more polite manner.

He raced at Bathurst again the following year but in the more popular Holden VP Commodore. Driving with David Brabham, they finished fourth.

Back to Europe he was a leading competitor in the 1995 and 1996 BPR series at the wheel of Luciano Della Noce's Enea team Ferrari F40 and took an outstanding victory on his home track at Anderstorp.

Olofsson's last full season was in 1997 and it saw him finish second overall and first in the GT1 class at Le Mans sharing a Gulf McLaren F1 with Jean-Marc Gounon and Pier-Henri Raphanel.

Olofsson retired from racing at the end of the year. Following his retirement, he worked in a management role for a number of teams in the Swedish Touring Car Championship and latterly as team manager of Elgh Motorsport team in the European, World and Swedish Touring Car championships.

He still took part in the odd race, usually in a friend's Ferrari in FIA GTs.

• 1977 - Swedish F3: Champion. European F3: 3 wins (Zandvoort, Osterreichring, Knutsdorp) 2nd overall.
• 1978 - Swedish F3: Champion. European F3: 4 wins (Nurburgring, Osterreichring, Knutsdorp, Kassel-Calden) 2nd overall.
• 1982 - 1987 Volvo Motor Sport works driver.
• 1986 Fuji 500 1st Johnny Cecotto and Anders Olofsson RAS SPORT VMS 240RXT, Le Mans March 86G Nissan R86V DNF
• 1987 Le Mans March-Nissan R88S DNF
• 1989 1st Japanese Touring Car Championship, Le Mans Cougar Nissan R88V DNF.
• 1991 Spa 24 Hours 1st
• 1990 Japanese Sports-Prototype Championship, Le Mans Nissan R89C DNF
• 1991 Le Mans Porsche 962C DNF 4th and 1991 Japanese Touring Car Champion, with M.Hasemi. Won Spa 24 Hrs (Nissan Skyline GTR) with D.Brabham & N.Hattori.
• 1993 Bathurst 1000 in a Nissan GT-R 6th
• 1994 Bathurst 1000 4th
• 1995 Bathurst 1000 Historics
• 1997 Le Mans 2nd overall, first in GT1