The driver was among those killed when the train derailed on Wednesday morning. The victims are yet to be formally identified, but officers are in close contact with their families. Six others were taken to the hospital with injuries described as not serious.
A number of emergency vehicles, including an air ambulance, were dispatched to the scene to assist with recovery efforts, and officers remain in the area.
"This is a tragic incident and first and foremost our thoughts are with the families and friends of those who have very sadly died this morning," Chief Superintendent Eddie Wylie said in a statement. "We remain on scene alongside our emergency service colleagues, and a major incident operation has been underway. I would like to reassure the public that this was not a busy service, and from CCTV enquiries and witness statements we believe all passengers have been accounted for. However, once the area has been made safe then a full and thorough search will be conducted, which is likely to take some time."
The authorities will investigate the exact cause of the derailment with the transport authorities, he said.
Heavy rain and thunderstorms disrupted some Scottish train routes overnight. Network Rail Scotland said they were assisting with the emergency response.
Scotland's First Minister, Nicola Sturgeon, described the derailing as an "extremely serious incident," and said that she was aware of early reports of serious injuries.
"My deepest condolences are with the loved ones of those who lost their lives in this tragic incident," Sturgeon posted on Twitter. "I have just been updated by Network Rail and the emergency services on the ongoing operation. My thanks go to them, and my thoughts remain with everyone affected."
Prime Minister Boris Johnson also expressed his condolences.
"I am saddened to learn of the very serious incident in Aberdeenshire and my thoughts are with all of those affected," he posted on Twitter. "My thanks to the emergency services at the scene."