At Wimbledon he upset the tournament 11th seed and word number 21, Guy Forget in the fourth round and lost in the quarter-finals to Stefan Edberg.

As a result of his Wimbledon success, Bergström qualified as one of sixteen players for the Grand Slam Cup, where he lost in the first round to Ivan Lendl.

He made his debut for the Swedish Davis Cup team in the World Group qualifying round against the Philippines in Manila.

[7] Bergström made his first ATP Tour final at the first tournament of the year in Adelaide losing to Goran Ivanišević in three sets.

[2] He made his second Davis Cup appearance for Sweden in the World Group quarter-finals against Australia, when he replaced Gustafsson for the reverse singles and then defeated Richard Fromberg.

Bergström begun 1993 by making the final in Adelaide for the second year running, losing to fellow Swede Nicklas Kulti.

Bergström also made the quarter-finals in Beijing and the semi-finals in Båstad and Toulouse and ended the year ranked number 52 in the world.

[2] 1994 started less successful for Bergström and he only reaches two quarter-finals prior to the French Open, where he lost in the second round of the qualifying event.

His first quarter-final was at the South African Open in Sun City, where he defeated his compatriot and the world number 10, Magnus Gustafsson.

Bergström's best result of the year was at Wimbledon where he reached the quarter-finals for the second time in his career, with victories over Diego Nargiso, Greg Rusedski, Jordi Burillo and Bryan Shelton, before losing to Boris Becker.

His best result was on the Challenger Tour, where he had to qualify for the main draw at the Tampere Open, and then made the final before losing to Galo Blanco.