The local men were detained over the killing of Newcastle University Medical School students Neil Dalton and Aidan Brunger, who were on the Malaysian part of the island on attachment to a hospital in Kuching.
The attack happened in the Jalan Padungan area of Kuching in Sarawak province, in the west of the Malaysian part of Borneo.
Deputy police commissioner Chai Khin Chung said: "We have finished our investigation, the crime has been solved. The suspects have been apprehended and they have admitted the crime. We have recovered the weapons from the crime.
"We are waiting for the corpses in the hospital mortuary to have the post-mortem carried out. We have all the major evidence in our hands which we will send to the prosecution."
He said the two students had got into an argument with the men at the table next to them in the bar and after leaving on foot they were followed by car and then attacked from behind.
"They came from behind and stabbed them", he said.
"The four people, who are local men, will be charged with murder. It's very unusual for Kuching, it's always very peaceful.
"It's very unfortunate and we were very surprised this kind of thing happened in our city."
Malaysia's The Star newspaper has said the main suspect is a 23-year-old fishmonger, another is a 29-year-old mechanic and the others, aged 19 and 35, and both unemployed. Two are said to have previous convictions for drugs and armed robbery.
The hospital where Mr Dalton and Mr Brunger had been working has been providing counselling to other students.
Sawatar Hospital medical director Dr Chin Zin Hing said the hospital was also working closely with the British Embassy to "see how best we can provide some assistance to the families of the men".