Jukka Kaski, a police superintendent, said Shkupolli was an immigrant who had been living for several years in Finland.
Kaski said the weapon used was an unlicensed handgun and that Shkupolli had killed his ex-girlfriend before heading to the shopping centre.
Speaking to Al Jazeera, Mia Ylonen, a journalist with YLE, Finland's national broadcaster, said: "Ibrahim Shkupolli had a long criminal history, he moved to Finland in 1990 and had several prior convictions from beatings, assaults and burglaries, and he had owned two illegal weapons previously.
"They [Shkupolli and his former girlfriend] had been together for 18 years and they split up last year, since then he has been threatening and bullying his ex-girlfriend and saying 'something bad will happen to you'.
"There has been a strong backlash against immigrants because of today's events because the man was from Kosovo and he was an immigrant himself."
Hundreds of people were at the shopping centre for New Year's Eve and witnesses said they erupted in panic when the gunman, dressed in black, began shooting.
Several ambulances were called to the scene and one witness said an employee had been seen lying on the floor covered in blood.
The shopping centre in Espoo, which is located 10km west of Helsinki, the capital, was evacuated and public transport services in the area rerouted.
The shooting is the country's third multiple shooting incident in as many years.
In September 2008, a lone gunman killed nine fellow students and a teacher at a vocational college before shooting himself in the western town of Kauhajoki.
In November 2007, an 18-year-old student fatally shot eight people and himself at a high school in southern Finland.
Finland, a nation of 5.3 million people, has 1.6 million firearms in private hands and ranks among the top five nations in the world in civilian gun ownership.