Alhaji Abubakar Rimi was born in 1940 in Rimi Village of Sumaila Local Government Area of Kano State, Nigeria. In the early 1960s he attended an instructor's course at the institute of Administration in Zaria. He obtained a General Certificate of education from the University of London. In 1972, he completed a diploma in international affairs at the London institute of World Affairs, and later obtained a master's degree in International Relations. He served as an instructor at the Clerical Training Center in Sokoto, and later became an Administrative Secretary at the Nigerian Institute of International Affairs.
Rimi was an independent candidate in the Federal Parlimantery elections for Sumaila Constituency in 1964 while Musa Said Abubakar was the NEPU Federal Parlimantary candidate for Sumaila Constituency they contested against Alhaji Inuwa Wada of the NPC but they all withdrew for Alhaji Inuwa Wada when they were jailed(see Chapter 10, page 204-of African Revolutionary The Life and Times of Nigeria's Aminu Kano by Alan Feinsten ISBN 978 156 299 4).
He was a member of the Constituent Assembly (1977–1978). In December 1978 he was elected the PRP's Deputy National secretary at the party's first national convention in Lagos. He was a PRP candidate in the 1979 General elections. Abubakar Rimi was elected to the governorship of the old Kano State as candidate for the PRP in the Nigerian Second Republic, a post he occupied from October 1979 – May 1983.
His Cabinet was termed the "All Graduate Cabinet". Alhaji Sule Hamma was appointed the SSG, Alhaji Abdullahi Aliyu Sumaila was Secretary of the Executive Council and Principal Secretary to the Governor,(PS to Governor) later serving as Rimi's Campaign Manager in the 1983 elections, Tijjani Indabawa was his Principal Private Secretary (PPS to Governor)and Sully Abu was Press Secretary to the Governor. He was said to be a liberal influence, promoting adult literacy and encouraging women to emerge from Purdah. He abolished the unpopular haraji (personal tax) and jangali (cattle tax), relics of the colonial period when the British governed through the emirs in the North. In 1980 he declared an annual worker's day. His suspension of the Emir of Kano led to riots in July 1981, followed by the killing of Rimi's political advisor Dr. Bala Mohammed. During the upheavals the offices of Triumph Newspapers, Radio Kano and several ministries were burned down.
In May 1983 Rimi fell out with his mentor Aminu Kano and moved from the People's Redemption Party (PRP) to the Nigerian People's Party (NPP) in preparation for the 1983 elections. He resigned from office and was replaced as governor by his deputy, Abdu Dawakin Tofa.
In 1993, Rimi accepted the post of Chairman of the Nigerian Agricultural and Cooperative Bank (NACB) under the Ibrahim Babangida administration. During the Nigerian Third Republic Rimi was a member of the Social Democratic Party (SDP) and one of the early supporters of the June 12 movement opposed to the annulment of the election of MKO Abiola. Later he left the progressive movement, and became Minister of Communications under the Sani Abacha Administration.
He was one of the founding members of the Peoples Democratic Party (PDP). He was the Chairman of the Finance committee of the Party at its inception and also one of its presidential candidates. He was appointed Chairman of the Nigerian Security Printing and Minting Company (NSPMC) in the first tenure of Obasanjo as a Civilian President. He later moved to the Action Congress (AC), but in 2007 Rimi returned to the (PDP). In December 2008, he called on the Chairman of the Independent National Electoral Commission, (INEC), Professor Maurice Iwu, to resign from office, citing irregularities in the previous presidential election.
In January 2006, his wife was killed at his home. His son was among those charged for the murder, but was later released due to lack of evidence and one of his nephew is still under arrest Mustapha .
On April 4, 2010, Rimi was accosted by armed robbers while returning to Kano from Bauchi state. Although unharmed, he seemed to have suffered a massive stroke and died shortly thereafter.