36-year-old Zaida Catalán was found dead with an American colleague and their Congolese interpreter.
The UN said it would conduct an inquiry into the deaths, the cause of which is not yet clear.
The experts and four Congolese nationals accompanying them were kidnapped two weeks ago in the conflict-ridden province of Kasaï-Central, where they had gone to investigate reported human rights abuses.
Swedish Prime Minister Stefan Löfven reacted to the news "with sadness and dismay", he said in a note.
Löfven said Catalán had worked tirelessly for peace and justice, that her mission "gave hope to a country that has long been plagued by violence" and that she risked her own life to save others.
"We share the despair of her loved ones, while feeling a deep gratitude for her contribution," he added.
Foreign Minister Margot Wallström wrote in a Tweet: "Appalled at Zaida Catalán's death. We mourn with her loved ones. Those responsible must be held accountable."
Green Party spokespeople Gustav Fridolin and Isabella Lövin described her as a "true role model" and added: "We will cherish tenderly the bright memory of her."
Fridolin and Catalán had worked together for two years as spokespeople for the Green Party's youth wing.
The bodies of Catalán and her colleague Michael Sharp were taken to a morgue at the airport of the provincial capital Kananga. The Swedish Foreign Ministry has no information about when Catalán's remains will be brough to Sweden.
The group was investigating and documenting human rights violations in the area, which has been seen violent conflicts since government forces last year killed local militia Kamwina Nsapu. Since then, hundreds of people have been killed in the unrest as tribal leaders have rebelled against the central government.
A spokesperson for the DRC government criticized the UN for failing to take adequate measures to protect the experts, saying it was "not normal" for foreign workers to come to the region.
“If the government had been informed of the activities of these officials, perhaps they would have had an escort for their safety,” said Lambert Mende.
The disappearance of Catalán and Sharp was the first time UN experts had been reported missing in Congo, Human Rights Watch reported, and was the first recorded disappearance of international workers in the Kasai provinces.
The Swedish foreign ministry has since 2006 advised against travelling to the DRC, where there is a conflict between security forces and militias.