Löfven told Parliament's Speaker on Friday that Sweden will be governed by a Red-Green coalition.
Between them, the Social Democrats and the Greens won the support of 38 percent of Sweden's voters in Sweden's elections on September 14th.
Before formally taking over as Prime Minister, Stefan Löfven must first be elected in Parliament and this not expected to take place before next Thursday.
His next task is to try and push through a new budget.
The opposition parties that made up Sweden's outgoing centre-right Alliance government have said they will abstain from voting on Löfven's election if it looks like he has garnered enough support for the budget. Some commentators had previously suggested that they would try to block his appointment.
Stefan Löfven is set to become Sweden's next Prime Minister. Photo: TT
To ensure budget approval, Löfven must convince the Left Party to back him, despite his decision to exclude them from government and ongoing disagreements over profits in the welfare sector.
The Left wants to stop private companies working with schools and hospitals from making profits. Neither the Social Democrats nor the Greens want an outright ban, although both have backed tougher regulation of businesses working with the public sector.
The leader of the Left Party Jonas Sjöstedt said on Friday that negotiations between his politicians and the Social Democrats were continuing.
He used a slightly different form of words when discussing his efforts to stop private companies linked to welfare from making a profit, leading many political journalists to conclude that he may tone down his approach in return for closer cooperation with the new coalition on other issues.
Li-Bennich Björkman, a Professor of Political Science at Uppsala University in eastern Sweden, told The Local that Löfven's rejection of the Left Party as a formal coalition partner may come back to bite him.
“I think it was a major mistake to not include the Left Party, because you can see that it was a huge disappointment to them, so much so that it could create difficulties in the future,” she said.
But she added that it was an “understandable” move, considering the “historical” bad blood between Social Democrat voters and the Left, which was formerly Sweden's Communist Party.
“Having said that, any minority government is dependent on support to get their proposals through, and I don't think the Left Party will have any other option than to side with the government most of the time. Who else can they turn to?” she said.
Left Party leader Jonas Sjöstedt. Photo: TT
It is uncertain how the anti-immigration Sweden Democrats, who all the other parties have so far refused to negotiate with, will vote on Löfven's budget.
Some experts argue that they will vote in favour of an alternative budget produced by the former governing Alliance, a move which could prompt a re-election.
But Professor Björkman told The Local she didn't think that would happen.
“The Sweden Democrats aren't interested in another election, they want the time to concentrate on boosting their own organisation first.”
Professor Björkman told The Local that things would also get interesting when it came to dividing ministerial posts between the Social Democrats and the Green Party.
“My guess would be that the Social Democrats are really going to fight for having the vast majority of the posts, emphasizing the Greens' rather low results as the justification,” she explained.
“On the other hand, the Greens have probably emphasized the fact that without them in government, Löfven might not be able to create a government at all, which could have meant new elections. These will be tough negotiations, especially considering the Greens have nothing to lose,” she told The Local.
“Also, I don't think the Social Democrats trust the Greens. They think they're inexperienced and don't think they're as responsible for running the country. I think this also makes them reluctant to give them many ministerial posts.”
Social Democrat leader Stefan Löfven, right, with the Green Party co-spokespersons. Photo: TT