The decision throws the government of Prime Minister Stefan Löfven into turmoil since his is budget certain to fail if it comes to a vote as is on Wednesday. If it does, Löfven has said he would not continue as premier under an opposition budget.
"In the current situation ... we will vote for the Alliance budget proposal," Karlsson told a packed news conference on Tuesday. "We don't trust the government's funding."
Holding the balance of power in parliament, the Sweden Democrats can sink the budget put forth by the Social Democrats and their allies the Greens by voting for the one put forward by the four-party Alliance.
Swedish politics allows each party or coalition to submit its own budget and the one that gathers the most votes wins. As it stands now, the Sweden Democrats backing of the Alliance budget will give it the support it needs to win.
Karlsson told reporters he wasn't worried that the party's decision might prompt a crisis of government and the ire of voters. He said the issue of immigration must be brought to the forefront of Swedish politics even if it means the Sweden Democrats lose their position as kingmakers in parliament.
"We are prepared to take the risk to bring up immigration on the agenda," Karlsson said.
But Löfven could still keep his government and some of his budget by sending it back to committee to be reworked to make it more palatable to the Alliance.
Anna Kinberg Batra, parliamentary group leader for the Moderates, was cool to any talk of compromise Tuesday night between the Alliance and the government. She told reports it was Löfven who is responsible for presenting a workable budget.
"There are significant differences between our budget proposals," she said. "It's not the opposition's responsibility to get through the government's budget."
Parliament will discuss and vote on the budget Wednesday morning.
Some were critical of the Sweden Democrats' decision, saying they were putting the stability of Sweden in doubt.
"They are playing some kind of game, a sort of power play," said Left Party Leader Jonas Sjöstedt to Swedish Television. "It's not just politics. It affects people, it affects those single parents who had won on this budget, it affects the railroads that would have been built. They risk Sweden's economy and stability for a power play."