"From receiving 10,000 asylum seekers per week, we now have - for over a year- fewer than 500 asylum seekers per week... and only a handful of them have come via southern Sweden," Sweden's interior minister Anders Ygeman said at a press conference in Stockholm.
But the removal of the ID checks on train, bus and ferry passengers before they travel into Sweden would be balanced by more thorough police checks once they arrive at the Swedish side of the border.
Ygeman said that the government would "intensify" the border controls carried out by police on the Swedish side of the border to cover everybody entering Sweden and also introduce automatic camera surveillance at the borders with number plate recognition and vehicle x-ray functions.
"With these stronger border controls, we have decided that the ID-checks can end," said Anna Johansson, Sweden's infrastructure minister. "The government would otherwise have had to decide to extend them after May 4th."
Johansson added that although the requirement for public transport companies to carry out ID-checks would expire from midnight on Wednesday, it was still unsure when the traffic would return to normal.
"This depends on several things: how fast the Swedish Transport Administration, the public transport companies and the police can end the controls, introduce new timetables and ensure that the border controls can be carried out adequately," she said.
The ID-checks were brought in on January 1 last year as a way of reducing the number of migrants seeking asylum in Sweden. Over the past year, the number of refugees coming to Sweden has fallen dramatically, partly as a result of a toughening of Swedish border and immigration policy, and partly as a result of the refugee deal signed between Turkey and the European Union.
The ID-checks have generated complaints from those who commute between Malmö and Copenhagen.
Per Tryding, deputy chairman of the Swedish Chambers of Commerce in southern Sweden, told Radio Sweden that his organisation estimated that the controls cost SEK 1.5 billion a year in lost working hours alone, equivalent to the value of Sweden's total annual music exports.
"A lot of people have stopped applying for jobs across the water, and in some cases, people have just quit their job without having a new one to go to, because with kindergarten times, it just doesn't work," he told Radio Sweden.
He said that he believed that the decision had come because of pressure from the European Commission, which saw the ID checks as transgressing the rules of the Schengen Agreement.