Kraft's coalition of centre-left Social Democrats (SPD) and environmentalist Greens will now take power in the western economic powerhouse, which has been politically paralysed for nine weeks following an inconclusive election result.
The outcome is a blow for beleaguered Chancellor Angela Merkel, whose centre-right federal government has now lost control of the upper house, or Bundesrat, which represents Germany's 16 states. This, in turn, will make it harder for her coalition of conservative Christian Democrats (CDU) and pro-business Free Democrats (FDP) to pass legislation.
Kraft, 49, won the second ballot with 90 MPs voting for her, 80 against and 11 abstaining.
In her first address as premier, Kraft thanked the previous centre-right government – which was resoundingly trounced at the polls in May – for its five years' service.
“Amid all the political differences, one goal unites us: a strong and liveable NRW,” she said.
As the leader of a minority government, Kraft will have a tough time passing legislation. Her “red-green” coalition will need to scrape together other parties' votes in the state parliament – either from its left or its right – meaning it will need to make deals or risk a parliamentary deadlock.
Kraft said she wanted to work with all parties to ensure the smooth governing of the state.
“We want to strive with all parliamentary parties to forge a new path,” she said. “Let us take this opportunity.”
But the CDU and FDP have said they will oppose the new centre-left coalition, meaning it may have to rely on the radically socialist Left party.
Despite the nine weeks of political wrangling in which innumerable coalitions were floated and then abandoned, Chancellor Merkel blasted Kraft's government as weak. She told daily Rheinische Post that Kraft had repeatedly stressed during the campaign that the state needed a strong, stable administration.
“Now she will start work by massively breaking her word. You can't trust such a government,” Merkel said.
Merkel brushed aside fears of gridlock in Berlin now that her conservative government has lost its majority in the Bundesrat. She said "important legislation" such as a €80 billion austerity drive to 2014 and a health care reform package would pass because they do not need approval by the states.
On other issues on which the upper house must give its blessing, such as a bid to extend the life of Germany's nuclear power plants, Merkel said she would reach out to specific state governments to hammer out a compromise.
Incessant squabbling over a range of policy issues including tax and health care reform have marred Merkel's nine-month-old government, costing it crucial poll support.