Bjarni was born in Reykjavík. After obtaining a law degree at the University of Iceland, Bjarni completed his studies in Germany and the United States before returning to Iceland to work as a lawyer.
The former Icelandic Prime Minister Bjarni Benediktsson was his great-uncle.
Bjarni entered the national parliament in 2003 and has been active in several committees in the areas of economy and taxation, industry and foreign affairs.
Bjarni was elected leader of the conservative Independence Party at its national convention on 29 March 2009 with 58.1 percent of the vote, about a month before the April 2009 Icelandic legislative elections. The party came in second in the elections with 16 seats, nine fewer than in the previous elections. After conceding defeat on 26 April 2009, Bjarni said his party had lost the trust of voters. "We lost this time but we will win again later," he said.
In the 2013 Althing elections on 28 April the Independence Party and their ally the Progressive Party each won 19 seats. On 17 May 2013 Icelandic media reported that Bjarni would take up the position of Minister of Finance and Economic Affairs in a cabinet led by Progressive Party leader Sigmundur Davíð Gunnlaugsson. In the 2016 Althing elections, the Independence Party won 21 seats, while the Progressive party only won 8. Shortly after the results, Prime Minister Sigurður Ingi Jóhannsson resigned from his post. A new coalition between the Independence Party, the Reform Party and Bright Future was formed in January 2017 with Bjarni designated to become Prime Minister.
In 2015, it was revealed that Bjarni had registered on Ashley Madison, a website for extramarital affairs. In response, Bjarni and his wife said that they had both registered on the site because they were curious. His username was "IceHot1".
As reported in 2016, Bjarni "shared what is known as 'power of attorney' over a shell company" involved in the Panama Papers.
Bjarni came under criticism in January 2017 for not revealing a government report on the offshore bank activities of Icelanders before the 2016 parliamentary elections. Bjarni falsely told reporters that he had not seen the report prior to the elections. He later apologized for his "inaccurate timeline".
Bjarni became Prime Minister of Iceland on 11 January 2017. In September 2017, the future of the Icelandic government and Bjarni's tenure as prime minister was put in doubt when the Bright Future party withdrew from the governing coalition. Bright Future did this in the wake of reporting that government ministers of the Independence Party had concealed that Bjarni's father, Benedikt Sveinsson, recommended that the criminal record of convicted pedophile Hjalti Sigurjón Hauksson be erased.
The Minister of Justice, Sigríður Andersen, had informed Benediktsson about his father's involvement in the letter of recommendation in July, and refused to disclose the recommendation's author until compelled to by a parliamentary committee.