The disaster in the Atacama area yesterday prompted the government to declare a state of emergency, which means the military take charge over civilian leaders.
It also forced a suspension of operations by Codelco, the world's biggest copper producer.
The death toll - a 34-year-old man and a 45-year-old woman - was provided by deputy interior minister Mahmud Aleuy.
Chile rushed in the army and urged people to flee as heavy rains flooded towns.
The torrential storms, which began late Tuesday and are unusual for the arid region, have left 700 people homeless, cut off roads, caused power outages and severed communications.
President Michelle Bachelet traveled to the region to coordinate relief operations.
About 40,000 people were without electricity and as many or more without potable water, officials said.
The rain flooded the main streets in the regional capital Copiapo and in several towns. It also cut off hundreds of residents in remote areas.
The weather forced state-owned Codelco to halt operations in Atacama and the neighboring region of Antofagasta.
"At this time, Codelco's operations are resuming slowly, as we constantly monitor weather conditions to ensure the safety of our people and equipment," said the company, which produces around 11 percent of the world's copper - 1.6 million tons a year.
Authorities declared a health alert for several municipalities.
Bachelet expressed solidarity with all those affected and said her government would send all necessary resources to the area.
The floods in the north came as southern Chile battled devastating wildfires exacerbated by a severe drought.
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