Two of the officers were identified last week and the process was completed for the remaining three on Tuesday.
"The goal was that every family should have their relatives back home. Now we are ready to finish our work in Kebnekaise," said Urban Johansson at the Swedish police on Wednesday.
The five officers have been named as Truls Audun Ørpen (46), Bjørn Yngvar Haug (40), Siw Robertsen (45), Steinar Utne (35) and Ståle Garberg (42), all of whom died in the crash on March 15th.
The Norwegian Air Force welcomed the news as the next stage of the farewell process.
"It is nice to get this confirmation, that the identification of one's kin has been completed. Then one can look further towards the next step to a final farewell when the time comes," said Eilev R.Pettersen at the Norwegian Air Force to the VG daily.
It remains uncertain however when the victims' bodies will be returned to Norway as the search for the remains of the deceased is ongoing.
"As it stands the work is continuing," said Kiruna area manager Håkan Alselind to broadcaster TV 2.
Some 50-60 people are involved in the work concerning the accident.
The identification process was carried out using DNA testing and the next of kin were informed of the results by the Norwegian authorities.
"There remains several weeks of analysis work for forensics until the work is complete," Urban Johansson said.
The accident investigation is being led by the Swedish Accident Investigation Board (Statens haverikommission - SHK) and it is not yet known when the cause of the crash will be established.
The crashed aircraft, a C-130 J "Super" Hercules transport plane manufactured by Lockheed Martin in the United States, went missing while flying in northern Sweden on March 15th 2012.
At the time, the Hercules was participating in the Cold Response military training exercise taking place over northern Norway which was scheduled to run from March 12th to March 21st and included 16,000 soldiers from 15 countries.