Varešanović started his career with Sarajevo, breaking into the first team in 1991, but getting only limited playing time. With the start of the Bosnian war, competitive football in the country halted and Sarajevo became a touring club. During one of these tours, Varešanović was spotted by Bordeaux scouts, and he quickly joined the French team. A year later he made a move to Olympiacos, spending two seasons with the Greek outfit. With Olympiacos, he won the Superleague Greece in the seasons 1996–97 and 1997–98. He next moved to Turkish Süper Lig side Bursaspor, who he would go on to represent on two separate occasions. In 2002 while back at Sarajevo, Varešanović won the 2001–02 Bosnian Cup. He concluded his playing career with Sarajevo in 2004.
After concluding his playing career, Varešanović was named Sarajevo sporting director, and held the position for two years. In 2010, he was named Sarajevo manager and led the team for one season and finished second in the 2010–11 Bosnian Premier League season. In the summer of 2011, he was approached by Velež Mostar, and went on to lead the Herzegovina outfit for also one season.
On 5 May 2014, Varešanović accepted an offer from Olimpik. In his second season, he won the Bosnian Cup trophy and made historic achievement with Olimpik by winning the first trophy for the youngest football club in the Bosnian Premier League. Varešanović left the club on 21 November 2015.
Return to Olimpik
Varešanović once again came back to Olimpik in June 2017, but again left the club the very same year in November.
On 26 February 2019, Varešanović signed a half-a-year contract with Bosnian Premier League club Tuzla City. His first win as Tuzla City's manager came on 9 March 2019, in 0–2 away win against Krupa. On 25 May 2019, after the end of the last game of the 2018–19 Bosnian Premier League season in which Tuzla City lost against Željezničar at home 0–3, Varešanović decided to leave Tuzla, stating: "I've been here for about three months, we have achieved what we had planned, but I will not be the manager of the club next season. I'm just too tired for this time, and some things have happened that have added to the decision of my deparutre, so..." He officially left the club a day later on 26 May.
