Known for his contributions to dynamical systems theory, he served as full professor at Instituto Nacional de Matemática Pura e Aplicada from 1980 to 2016.

Melo wrote numerous papers, one being a complete description of the topological behavior of 1-dimensional real dynamical systems (co-authored with Marco Martens and Sebastian van Strien).

[1] He proved the global hyperbolicity of renormalization for Cr unimodal maps (co-authored with Alberto Pinto and Edson de Faria).

He adopted mathematics after attending a course in the researcher of the Elon Lages Lima Institute in a colloquium in Poços de Caldas, Minas Gerais.

Invited by Elon to study at Instituto Nacional de Matemática Pura e Aplicada he moved to Rio de Janeiro with his wife Gilza in 1970, with Jacob Palis his advisor, where Welington completed his doctorate in two years, with a thesis published in the prestigious Inventiones Mathematicae in 1972.