Shannon Brent Flewellen, a 28-year-old fisherman, and a 31-year-old unemployed former Westport man were arrested this week and charged with Mr Kim's murder.
Police are expected to apply for them to be remanded in custody when they appear in court today.
Inquiry head Detective Inspector John Winter said police were still looking for others who may be involved in the slaying.
They were also focusing on finding Mr Kim so that his remains could be returned to his family.
"They are devastated. They always held out hope that somehow there would be a miracle ... They suspected the worst but hoped for the best," he said.
Mr Winter said police believed Mr Kim was killed at Charleston, 27km southwest of Westport, and they knew how he died.
Following a tip-off, police are searching an area of dense bush near Charleston, the Nelson Mail said today.
Police reopened the investigation into Mr Kim's disappearance in May as part of their routine practice to revisit unsolved missing persons cases. He was last seen in Nelson in September 2003 and reported missing in May 2004.
Police had been able to access money from Mr Kim's bank account and that had been returned to his family along with a donation from Victim Support.
Police said Mr Kim's brother would use the funds to come to New Zealand.
