He was born on 2 July 1958 in Belgrade.

He graduated from the Faculty of Mechanical Engineering, where he also obtained his PhD in industrial robotics in 2000. He worked as a teaching assistant at this faculty during the period 1984-1990. 
            
He worked as an engineer at the machine tool factory “Ivo Lola Ribar” in Belgrade, and then at REIK “Kolubara”. He was chosen as the chief executive officer of DP “Proleter” in 1990. He is credited with reconstructing this company and by changing its name to “FMP”, creating a brand. He was also the President of the SC of MDD “FMP” Belgrade, President of the Steering Committee and Assembly of “FMP”, President of FMP GROUP.

He was elected as the Deputy President of the EB of the Assembly of Belgrade for Economy and Finance in 1992. He became President of the City Government in 1993, and one year later was chosen for Belgrade City Mayor, remaining in this position until 1997 (23 June 1994 – 21 February 1997). He was also a deputy in the National Assembly of the Republic of Serbia, for two terms. After the elections in 2000 he was also a deputy in the Federal Assembly on the list of the Democratic Opposition of Serbia.

In Zoran Đinđić’s Government (25 January 2001 – 18 March 2003) he was a Vice-President and Deputy Prime Minister, working on rather complex issued in resolving the conflict in the south part of central Serbia as the President of the Coordination Centre for the South of Serbia and Coordination Centre for Kosovo and Metohija. During the period from 12 March 2003 until 17 March 2003, he was Acting Prime Minister of Serbia, and during the period 18 March 2003 – 3 March 2004, Deputy Prime Minister of the Government of Zoran Živković.

Nebojša Čović is the founder and first Vice President of KK FMP, and has also been the President of the Basketball Federation of Yugoslavia 1995-1997.

During his mandate the Yugoslav national team returned to the international scene in 1995, in Bulgaria, and later won the title of European Champion in Greece. One year later, the national team also played in the finals of the Olympic Games in Atlanta, and during that period the Basketball Federation gained a new home – the “House of Basketball” in Sazonova Street in Belgrade.

KK FMP was ABA League champion twice, won the Radivoje Korać Cup multiple times, was a semi-finalist of the ULEB Cup, finalist of the FRY championship and Super League of Serbia, and double champion of the junior EuroLeague.

It has been the champion of FRY and Serbia multiple times in all youth categories (pioneer, cadet, junior), and won numerous international tournaments.

During the past decades KK FMP has developed an image of a club that has shaped and promoted a large number of players through its system of work and development. They helped the club achieve excellent results, and later had great success across Europe both as part of the national team and as players in the best clubs in Europe: Miloš Teodosić, Zoran Erceg, Ognjen Aškrabić, Miroslav Raduljica, Nemanja Aleksandrov, Milan Mačvan, Duško Savanović, Dejan Milojević, Veselin Petrović, Marko Marinović, Bojan Popović, Mladen Šekularac, Vladimir Radmanović, Mile Ilić, Aleksandar Rašić, Branko Jorović, Branko Cvetković, Nemanja Aleksandrov, Nikola Vasić, Dejan Musli, Marko Jeremić, Dragan Apić...

As of 12 August 2011, he is President of KK Crvena Zvezda.

Taking a club that was on the brink of existence, through great work and effort, with proper organisation, good support by KK FMP which was at that time (courts, college, coaches and players) a leader and a unique example in the region for its method of work and organisation, he soon managed to consolidate one of the biggest clubs in the region.

During this past period, KK Crvena Zvezda, with its President Nebojša Čović, has established as the most stable, transparent and successful club in the region, and a regular EuroLeague member.

During this period KK Crvena Zvezda won 6 ABA Leagues, the ABA League Supercup, 7 national cups and 8 titles of Serbian champion. The younger teams of KK Crvena Zvezda that were made fully functional after the arrival of Nebojša Čović to the club have won a large number of national titles in all youth categories, and the Crvena Zvezda juniors became EuroLeague champions in 2014 in Milan, and played two more times in the finals of this competition in Madrid and Berlin.

Furthermore, in addition to the successes another highly recognisable point regarding the work of Nebojša Čović in basketball is the large number of players from junior sections promoted to the first team, and later in national team, such as Nedović, Gudurić, Dobrić, Simanić, Radanov, Ristić… while many players in the senior team gained true affirmation wearing the Crvena Zvezda colours, such as Kalinić, Jović, Marjanović, Cirbes, Kuzmić, Nikola Topić.

Some players have returned in their prime and once again wore the jersey of Crvena Zvezda, such as Igor Rakočević, while during past years some of the greatest names in world basketball wore the Crvena Zvezda jersey: Miloš Teodosić, Facundo Campazzo, Luca Vildoza, Tarence Kinsey, Stratos Perperoglou, Marcus Williams... considerably increasing the reputation of the club, not only in Europe, but worldwide.

In April 2017 he became the first foreign national to be given the honour of opening the International Sports Fair in Beijing, where he presented the concept and unique system of running a basketball club in front of several thousand guests and the most powerful people in Chinese sports.

He still holds the post of President of KK Crvena Zvezda mts, a club that has transitioned during these 13 years from the brink of bankruptcy to a stable club that has its own system and is successful across all categories. During the period between 2011 and today, KK Crvena Zvezda mts has won 22 trophies in all senior competitions, while the first team has become a regular EuroLeague participant. This period is considered to be the most successful in the history of the club, and Nebojša Čović its most successful president.

Nebojša Čović has been married for many years to his wife Vesna, he is the father of two children, and grandfather to four grandchildren.