He began composing as a young student in 1917, and his first known work was "La Cumparsita", which he wrote on the piano of the Federación de Estudiantes of Uruguay [1] Archived April 20, 2014, at the Wayback Machine.

In 1931, he collaborated on the film score for Luces de Buenos Aires, shot in Joinville-le-Pont, France, and starring renowned tango vocalist Carlos Gardel.

The most famous classic tango of all times is "La Cumparsita", written by Matos Rodríguez in 1916, with lyrics added later by Pascual Contursi and Enrique Pedro Maroni.

Matos Rodríguez also composed pieces for theater plays premiered in Buenos Aires, among them Manuel Romero's El Gran Circo Rivolta.

Other tangos composed by him include: “Che papusa, oí”, “Son grupos”, “Yo tuve una novia”, “Cuando bronca el temporal”, “Hablame”, “Pobre corazón”, “Haceme caso a mí”, “Canto por no llorar”, “Rosa reseca”, “Botija linda”, “El pescador”, “Te fuiste, ¡ja, ja!”, “Adiós Argentina”, “Mi provinciana”, “La milonga azul”, “Dale celos”, “Raspail”, “Mocosita”, “La muchacha del circo”, and “San Telmo”.