Varela studied Humanities and Education at the National University of San Marcos where she met other future writers such as Sebastián Salazar Bondy, Javier Sologuren, Jorge Eduardo Eielson, and her future husband, the artist and sculptor Fernando de Szyszlo with whom she had two children.
In 1949 they traveled to Paris where she met Octavio Paz, a key figure in her life, who introduced her to the artists and intellectuals there, such as André Breton, Jean-Paul Sartre, Simone de Beauvoir, Henri Michaux, Alberto Giacometti and Fernand Léger, among others; and also other Latin American authors who lived in France at that time, for example Carlos Martínez Rivas.
While in Paris, Varela was part of the group of expatriate Latin American artists and writers who met regularly at the Café de Flore, engaging in vigorous discussions on how they could participate in the international modern movement while preserving their Latin American cultural identity.
Paz persuaded her to publish her poetry, and in the preface to the first edition of her debut book Ese puerto existe (1959), he wrote: "At that time we all used to sing.
This attempt to find perfection with every new poem has, according to Mario Vargas Llosa who used Varela's poem Ternera acosada por tábanos (Calf tortured by horse-flies)[3] as a notable example of her philosophy, "the quality of heroes from ancient myths who die, but fight to the very last moment anyway."