When Germany divided after World War II, a group of West German clubs re-established the pre-war German football association, the DFB. Meanwhile, East Germany established its own association, the DDR-Oberliga. Barring the occasional meeting between the East and West German national teams in international competition, the two were kept largely separate until November 1989, when growing support for reunification led both associations to allow unrestricted competition across the two leagues.
Thom had been a key player for East Berlin club BFC Dynamo since joining them in 1983. In 1984, he won the first of five consecutive league titles with the club, to which they also added two East German Cups (1988, 1989). A forward, he was the DDR-Oberliga's top scorer for the 1987-88 season and was named the 1988 East German Footballer of the Year.
Toward the end of 1989, he received permission from the DDR-Oberliga to move across the border, the first East German player to do so (though there had been defections, including three footballers from the East German national team earlier that year) . He struck a deal with Bayer Leverkusen and, on 1 January 1990, joined them for a fee of 3.6 million German marks.
He enjoyed a lengthy career with Leverkusen, making 161 appearances between 1990 and 1995, when he moved to Celtic for £2.2 million. He returned to Germany in 1998, signing for Hertha Berlin, and retired in 2001.