At Brøndby, Høgh was re-schooled from his midfielder role to a central defender, who from time to time took part in the attacking moves. He was one of several new players from Jutland clubs who arrived at Brøndby that year, including Marc Rieper who Høgh would later spend the majority of his Danish national team matches partnering in the Danish central defense. Despite personal success, with Høgh being named 1993 Brøndby Player of the Year, the club only won a single Danish Cup trophy in his time at the club. In his last year at Brøndby, Høgh suffered minor injuries and he lost his place in the starting line-up for both club and country. In November 1994 he moved back to AaB on a three-year semi-professional contract. He played the second half of the 1994–95 season, as AaB won the Danish championship. He also played full-time in all three matches, as the Danish national team won the 1995King Fahd Cup. Following the title wins, Høgh moved abroad to play for Fenerbahçe in Turkey, for 11 million DKK in June 1995.
Moving abroad
In his first year at Fenerbahçe, he and former Brøndby player Uche Okechukwu formed the defensive duo, in a season that ended in the first Turkcell Super League championship for the club in seven years. He is still an unforgettable defence player for Fenerbahce Fans. In the meantime, Høgh had re-entered the Danish national team starting line-up, and he played full-time in Denmark's three matches at the UEFA Euro 1996. He also appeared in all Denmark's five matches at the 1998 FIFA World Cup, before he transferred to English club Chelsea for 3.5 million DKK in July 1999. At Chelsea, Høgh was a back-up player to French internationalsMarcel Desailly and Frank Leboeuf. He won the 2000 FA Cup with the club, contributing two appearances to Chelsea's victorious campaign, and he was also called up for Denmark to play the UEFA Euro 2000 tournament, though he sat out in all games through injury. He played 17 matches for Chelsea, 9 in the league, until an ankle injury forced Høgh to retire in March 2001. In January 2007, Høgh suffered an intermediate stroke while at a hotel room in Copenhagen. He was talking to his wife on the phone at the time, and was quickly aided by paramedics. He was also unable to move any of his right side and couldn't speak afterwards. During his recovery, he received moral support from both his former clubs Chelsea and Fenerbahce.
