Lawmakers elected Guy Parmelin of the SVP to the government, replacing Finance Minister Eveline Widmer-Schlumpf, who resigned.
Switzerland's federal council posts are traditionally shared among the major parties from right to left under a tacit decades-old agreement, dubbed "the magic formula" aimed at ensuring political stability.
The SVP argued that it had been short-changed under this formula since 2007, when it lost a slot despite its rising popularity.
The rightwing SVP posted a record performance in the October 18 polls, winning 65 of the 200 seats in the lower house, an increase of 11 from the previous vote.
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Widmer-Schlumpf did not disclose the reasons for her departure, but her position on the council had become increasingly politically untenable.
She was once a member of the SVP's moderate wing and in 2007 beat out the party's firebrand billionaire leader Christoph Blocher for a government seat.
The SVP then kicked her out of the party, but she held onto her seat under the Conservative Democrats' banner, a party she created which claimed just four percent support in October.
After winning 29.4 per cent of the vote, the SVP intensified its calls to reclaim a second federal council seat.
The other parties represented in the federal council are the centre-right Liberal Party, the Socialists and one representative from the centrist Christian Democrats.
Meanwhile, Johann Schneider-Ammann of the Liberals was elected as president of the Swiss federation for the next 12 months.
The rotating position has limited powers and alternates each year between the seven government ministers.
Schneider-Ammann, also the minister for the economy, will formally replace Justice Minister Simonetta Sommaruga of the Socialist Party as president at the end of year.