"I'm not interested in being the administrator of the crisis in the OAS, but rather the facilitator of its renewal," he said after the vote.
Almagro, who was elected to a six-year term by a vote of 33 in favor with one abstention, ran unopposed, after securing the support of key countries. He replaces Jose Miguel Insulza of Chile on May 26.
His election comes just weeks before a Summit of the Americas in Panama that will include Cuba for the first time in decades.
"The days of a discursive, bureaucratic OAS, removed from the concerns of the American peoples, anchored in the paradigms of the last century, is definitely giving way to an OAS of the 21st century," he said.
The United States, which funds more than half the OAS budget, wants changes that will help it regain ground lost to other groups as the go-to forum for resolving regional crises.