Born to Serbian parents in Ljubljana, Ačimovič started his career in the youth ranks of Železničar Ljubljana. He made four first division appearances for Železničar when he was 18 years old. From 1996 until 1998 he scored seven league goals in 36 matches for Olimpija. He then joined Red Star Belgrade, where he played for four and a half years. After successful appearances for the Slovenian national team in Euro 2000 and World Cup 2002, several bigger European clubs expressed interest in him. In the summer of 2002, he joined Tottenham Hotspur. In his first season in London, he made a few appearances, but never established himself as a first team player. In his second season, he became a fringe player.