Perasović was born in Stobreč, at that time in the SFR Yugoslavia, to parents Gašpar and Vica Perasović. He started playing basketball at age 14.[citation needed]
Perasović's club, KK Split, went on to win three EuroLeague championships, in 1989 and 1990 as "Jugoplastika", and in 1991 as "Pop 84". In 1988, 1989, 1990, and 1991, they also won the Yugoslav League championship. In 1990 and 1991, they also won the Yugoslav Cup, and in 1992, the Croatian Cup.[citation needed]
In 1997 he moved to the Spanish club Fuenlabrada, where he played until 2002. He then moved to the Spanish club Alicante, and retired from his basketball playing career in 2003. During his playing career in Spain, he won the Spanish ACB League Top Scorer award five times. He was also once the best scorer of the Radivoj Korać Cup, and he participated in Liga ACB All Star games.[citation needed]
In the 2007–08 season, Perasović was appointed the head coach for Estudiantes, filling in for Mariano de Pablos, who had been fired due to negative results.[citation needed]
He then moved to Zagreb, to become the head coach for Cibona. In 2009 he led the team to the Adriatic League final, winning the award for the best coach in the Adriatic League in that season, and won the Croatian Cup and Croatian League championship, respectively. He again took Cibona to the Adriatic League and Croatian Cup finals in 2010. He also won the Croatian League championship.[citation needed]
In January 2012, he came back to Spain to coach Valencia. Perasović won the 2013–14 EuroCup, and left the club in January 2015.[1] In March 2015, Perasović took over the senior Croatian men's national team.[2][3] After a disappointing EuroBasket 2015 tournament, in which Croatia was defeated in the round of 16, Perasović and Croatia parted ways.[citation needed]
In June 2015, he came back to Spain to coach Laboral Kutxa,[4] while in February 2016, he extended his contract with Baskonia through the 2016–17 season.[5] After being a semifinalist of the three competitions Baskonia played (EuroLeague, Copa del Rey, and Liga ACB), Perasović left the club and went back to coach Anadolu Efes.[6] On 16 December 2017, Anadolu Efes parted ways with him.[7]
On 16 November 2018, he came back to Spain to the third time to coach Kirolbet Baskonia until the end of 2019–20 season to replace Pedro Martínez.[8] On 20 December 2019, following a loss to Real Madrid, Perasović was fired from Baskonia.[9]
Note: The EuroLeague is not the only competition in which the team played during the season. He also coached in domestic competition, and regional competition if applicable.