National politics
Sverdrup was elected to the Norwegian Parliament in 1877, representing the constituency of Nordre Bergenhus Amt. He was re-elected in 1880 and 1883, and joined the newly established Liberal Party, of which his uncle Johan was the founder and chairman. When the Liberal cabinet Sverdrup took over in 1884, Jakob Sverdrup was a candidate for the position as Minister of Education and Church Affairs. However, due to King Oscar II opposing this, Sverdrup was instead appointed a member of the Council of State Division in Stockholm, effective from 26 June 1884.
However, already on 1 August 1885 Sverdrup was appointed Minister of Church Affairs, replacing Elias Blix. He held this position for a year, but had already become embroiled in controversy. In June 1885 the Norwegian Parliament had voted over whether to grant a poet's pension to the novelist Alexander Kielland. A Christian conservative wing of the Liberal Party, informally spearheaded by Lars Oftedal, stopped this proposition together with the Conservative Party. Kielland was seen as undermining Christian authority and morale in general. The decision was lambasted by Bjørnstjerne Bjørnson, who personally sent a similar application the next year; when it was voted down, Bjørnson protested by renouncing his own poet's pension. A commentator in the liberal newspaper Verdens Gang stated that Jakob Sverdrup was the true mastermind of his uncle's cabinet. The newspaper also speculated on a possible split of the Liberal Party, citing the Kielland case as a part of a broader trend that the Liberal Party failed to actually reform society in a liberal direction. Talks of "Moderate" and "True" Liberals had surfaced already ahead of the 1885 election.
When installed as Minister of Church Affairs, then, Jakob Sverdrup tried vigorously to establish so-called parish councils, increasing the local democracy in the Church of Norway, but he was voted down by the "True" Liberals in Parliament who in this case sided with the Conservative Party. Several cabinet members demanded Sverdrup's resignation, but instead he was transferred to the post as Minister of Auditing on 31 July 1886, allowing Elias Blix to return as Minister of Church Affairs. However, the controversy continued to grow, and in 1888 the cabinet members Hans Rasmus Astrup, Birger Kildal, Sofus Anton Birger Arctander and Elias Blix withdrew from their positions in protest. Thus, on 24 February 1888 Sverdrup returned as Minister of Church Affairs, holding two posts for a while before a replacement as Minister of Auditing was found on 4 March 1888. On 12 July 1889 the cabinet Sverdrup fell. The Liberal Party had been split, with a breakaway faction forming the Moderate Liberal Party, and this gave way for the Conservative first cabinet Stang.
In 1890 Jakob Sverdrup moved from Nordre Bergenhus Amt to become a vicar in Bergen. Nonetheless, he was placed on the party ticket in his old county Nordre Bergenhus Amt for the forthcoming election. He was thus elected twice, in 1892 and 1895, but now belonged to the Moderate Liberal Party. Following the latter election Jakob Sverdrup was twice asked by King Oscar II to form a new cabinet, but the efforts failed. Instead, the Conservative-Moderate first cabinet Hagerup assumed office on 14 October 1895, where Jakob Sverdrup was appointed Minister of Church Affairs for a third time. He held this position until the first cabinet Hagerup fell on 17 February 1898. The same year he was appointed as the new bishop of the Diocese of Bjørgvin; however, he never actually assumed the office due to health problems. He died in June 1899.
Sverdrup was decorated with the Royal Norwegian Order of St. Olav in 1885 and was a Commander of the Swedish Order of the Polar Star.