Amosun was born on 25 January 1958 to a Muslim family. He attended primary school at African Church Primary school in Abeokuta (1965–1970), and then African Church Grammar school, Abeokuta (1971 – 1977). He then went to Ogun State Polytechnic, graduating with a Higher National Diploma (HND) in 1983. Amosun gained an Associate membership of the Institute of Chartered Accountants of Nigeria (ICAN) in 1990. He became a fellow of the Institute in 1996. He also became an Associate member of the Chartered Institute of Taxation of Nigeria (1998).
Amosun began his career as an audit trainee with Lanre Aremu & Co. (Chartered Accountants) 1984. Later he joined XtraEdge Consulting as a managing consultant. From 1990 he was Principal partner of Ibikunle Amosun & Co. (Chartered Accountants) in Lagos. Amosun went to the University of Westminster in London, United Kingdom, where he acquired a Master of Arts in International Finance in 2000.
In April 2003, Ibikunle Amosun was elected to the senatorial seat of Ogun Central Senatorial district. He was an unsuccessful candidate to become Governor of Ogun State in April 2007, running on the All Nigeria People's Party (ANPP) platform, but was defeated by Gbenga Daniel. He disputed the result, but in August 2009 the Ogun State Election Petitions Tribunal dismissed the petition.
Amosun was the candidate of the Action Congress of Nigeria (ACN) for April 2011 Ogun State gubernatorial election. A report in the Nigerian Tribune on 12 February 2011 quoted his media aide as saying he had switched to the Congress for Progressive Change (CPC), but this was denied by ACN officials. Amosun won the 26 April election running on the ACN platform with 377,489 votes. Adetunji Olurin of the People's Democratic Party (PDP) polled 188,698 votes and Gboyega Isiaka of the PPN came third with 137,051 votes.
In 2015 Amosun stood for a second term as governor. He chose, Yetunde Onanuga, as his running mate of the state governor. He had to find a new running mate as his previous deputy governor had defected to an opposition party. Amosun chose Onanuga who had been working in the Lagos State Ministry of Environment over three other possible candidates.