"I actually audibly cheered," British data expert Nick Nilsson-Bean tells Radio Sweden of his reaction to the news.
German programmer Tobias Richter says his only regret was that he had already left Denmark when the news came out, so he couldn't buy any champagne in Denmark.
"It's a reason to celebrate for me. I commute most days in the week and it's really been horrific."
The last ID check was scheduled to be carried out at 11.46pm on Wednesday night.
But uncertainties remain as to what the intensified border controls on the Swedish side will look like after Swedish border police complained on Wednesday that they had received little warning of the intensified policing, which Swedish interior minister Anders Ygeman announced at a press conference on Tuesday evening. Ygeman estimates that the measure will cost SEK 60 to 80 million.
Michael Randropp from Denmark's Kystbanan commuter organisation, said that it would make a big difference if Swedish police mounted trains in Copenhagen and checked passports on the journey to Sweden, rather than forcing people to wait.
And commuter Nilsson-Bean said he thought that whoever designed the system should be identified.
"The whole system has been catastrophically badly thought out and quite frankly whoever put this in place needs to be pulled in front of some sort of committee to be questioned because it's awful. It's been terrible."