Gayibov was born in Baku on April 24, 1979. In 1995, he graduated from Baku Secondary School as No 1. In the same year, he entered as a Business Management faculty of Azerbaijan Institute of National Economy Management under the Cabinet of Ministers of the Republic of Azerbaijan.
In 1999, he obtained a Bachelor's degree in Business Management and graduated from a Master's degree in 2001.
Gayibov obtained his Ph.D. at the National State University of Physical Education, Sports and Health named after P.F. Lesgaft (St. Petersburg, Russia) in 2014.
He was accepted into the MEMOS XXIV Executive Master Program (Executive Masters in Sports Organization Management) in 2021. The program is supported by the International Olympic Committee, Olympic Solidarity and European Olympic Committees.
Gayibov worked at the storehouse of the "Balakhanineft" Oil-and-gas Production Office of the State Oil Company of the Republic of Azerbaijan (SOCAR) from 2000 to 2001.
In 2001–2003, he took up the post of an economist at the planning department of the "Balakhanineft" Oil-and-gas Production Office of SOCAR.
In 2003-2005, Gayibov worked as the Sports and Logistics Manager at the Azerbaijan Gymnastics Federation (AGF).
During these years, he took an active part in the Local Organizing Committees of 3 World Cup events (2003/04/05) and the 27th World Championships (2005) in Rhythmic Gymnastics, as well as in the organization of International Judges' Course (2007) in Artistic Gymnastics held in Baku.
He worked as the AGF General Manager in 2005-2006.
Gayibov was elected as AGF's Secretary General at a regular election conference of the organization in 2006.
In 2006–2007, 2008–2009, and 2013–2014, he acted as an Executive Director (from Azerbaijan) within the Local Organizing Committees of 3 European Championships in Rhythmic Gymnastics (2007, 2009 & 2014) held in Baku.
He was elected as the FIG Council Member (within 2008-2012 Olympic Cycle) at the 77th FIG Congress (Helsinki, Finland, October 17–19) in 2008.
He was re-elected as a Secretary General of Azerbaijan Gymnastics Federation at its Executive Committee's Meeting on December 25, 2010.
Gayibov was re-elected as the FIG Council Member at the 79th FIG Congress (Cancun, Mexico, October 25–27) in 2012.
He was elected as the Vice-President of the European Union of Gymnastics (UEG) at its 25th Congress in Portorose (Slovenia, December 6–7) in 2013. Consequently, he resigned from the membership of the FIG Council.
Since 2013, he is a member of the National Olympic Committee of Azerbaijan (NOC).
Gayibov was the organizer of the FIG Rhythmic Gymnastics Academy Level 1 (2013) and Level 2 (2014) for Coaches, held in Baku in 2013 and 2014.
In 2014–2015, he took up the position of the Executive Director of the Local Organizing Committee of the Open Joint Azerbaijan Championships (2015) in 6 gymnastics disciplines held as a Test Event for the Baku 2015 First European Games.
He was an adviser on gymnastics disciplines competitions held within the framework of the Baku 2015 First European Games within 2014-2015.
Gayibov was re-elected as AGF Secretary General at its Executive Committee's Meeting on December 24, 2015.
In 2015–2016, he was an Executive Director of the Local Organizing Committees of the FIG Artistic Gymnastics Individual Apparatus ("Challenge" in 2016) World Cup AGF Trophy, FIG Rhythmic Gymnastics World Cup AGF Trophy, and FIG Trampoline Gymnastics World Cup AGF Trophy held in Baku in 2016 and 2017.
In 2016–2017, Gayibov acted as Executive Director of the Local Organizing Committee of the Rhythmic Gymnastics Intercontinental Judges' and International Judges' Courses, Men's Artistic Gymnastics International Judges' Course, and the FIG Council of the 4th Islamic Solidarity Games, which took place in Baku in 2017.
He has great experience in sports events' organizations on the National and International level in Rhythmic Gymnastics, Men's Artistic Gymnastics, Tumbling, and Acrobatic Gymnastics, from 2003; Women's Artistic Gymnastics, Trampoline Gymnastics, and Aerobic Gymnastics, from 2013.
Gayibov was a delegate of the UEG and FIG Congresses; member of the delegation for the Olympic Games (Beijing 2008, London 2012, and Rio 2016); head of the Azerbaijani official delegations in different gymnastics disciplines during the European and World Championships; President of the Appeal Jury at different European Championships in gymnastics disciplines (as assigned) from 2014 to 2018.
He has been elected as the President of the European Union of Gymnastics (UEG) at its 27th election of Congress, held in Split, Croatia, on December 1–2, 2017. Consequently, Gayibov resigned from the position of AGF Secretary General. Since 2018, he has been acting as the UEG President (renamed into European Gymnastics since April 1, 2020) and is automatically a member of the FIG Executive Committee.
Gayibov attended the Tokyo 2020 Olympic games as a member of Jury of Appeal of gymnastics events
He was awarded the FIG Bronze Distinction as a twice-elected member to the FIG Council (2008 and 2012) at the closing of the 81st Congress of the FIG in Tokyo, Japan, in October.
Gayibov was awarded the FIG "Recognition" Medal by this organization at the 17th FIG Council, which was held in Baku in 2017.
On December 18, 2017, he was awarded the "Honorary Diploma of the President of the Republic of Azerbaijan" for his contribution to the development of sports in our country according to the order of the President of the Republic of Azerbaijan Ilham Aliyev.