Samoura, 54, comes from outside the football world, having worked with the UN for 21 years. She is currently based in Nigeria for the UN Development Program.
Samoura will take her post by mid-June after undergoing an eligibility check administered by an independent review committee.
FIFA president Gianni Infantino, who announced her appointment by the FIFA Council during a congress in Mexco City, said Samoura was a "great person" with experience managing big organisations, budgets and staff.
"We have to be serious when we say we embace diversity and we believe in gender equality," Infantino said.
"She will bring a fresh wind to FIFA, somebody from outside, not somebody from inside, not somebody from the past but somebody new."
Her appointment was a huge surprise at a congress that was meant to focus on confirming reforms aimed at cleaning up an organisation ensnared in a massive corruption scandal.
FIFA congress seeks to clean up mess
FIFA president Gianni Infantino opened a congress on Friday to confirm reforms at world football's scandal-tarred organisation.
Infantino was presiding over a gathering in Mexico City aimed at formally implementing changes that were adopted at an extraordinary congress in February to overcome a deep corruption crisis.
"Today we pass from the words to the actions, from the proclamations to the facts," Infantino said.
"You will see us reborn with a congress (in which) what we say, we are doing it as well, for the good of FIFA and for the good of football."
The former secretary general, Jerome Valcke of France, was sacked in January and banned from football for 12 years over misconduct in television deals and World Cup ticket sales - one of the many scandals that hit FIFA.
Germany's Markus Kattner has been serving as interim secretary general since then.
Infantino - who was elected in February after his predecessor Sepp Blatter was brought down by the corruption scandal - wants to turn the page and put the focus back on football.
In another step towards restoring trust, the North and Central American and Caribbean football confederation (CONCACAF), which has been in the eye of the corruption storm, elected a new president on Thursday.
Canadian football chief Victor Montagliani became CONCACAF's fourth president in five years after his three predecessors were ensnared in corruption allegations, with the last one arrested in December.
FIFA's new council, meanwhile, decided on Tuesday to resume the process to select the host of the 2026 World Cup, which had been frozen since last year over claims of misdeeds in awarding the tournaments to Russia for 2018 and Qatar for 2022.
