As noted by the late lamented Dicho, the lyrics of the song stem from the versos of the great Cuban poet, José Martí, first published 1891, the second of three poetical works by that author:
Versos sencillos

Also in his third volume:
Poesías dispersas- 1868-1895
It has been reprinted several times in compilations of Martí's poetry, notable Obras Completas, Edición Critica, published La Habana, Centro de Estudios Martianos, 2000-2003, and Poesía Completa, Ed. de Carlos Javier Morales, Madrid: Alianza Editorial, 1995.

In the several versions of Guantanamera, ony the first verse of Versos Sencillos is constant:
1
Yo soy un hombre sincero
De donde crece la palma,
Y antes de morirme quiero
Echar mis versos del alma
2
Yo vengo de todas partes,
Y hacia todas partes voy:
Ante soy entre las artes,
En los montes, monte soy.
3
Yo sé& los nombres axtraños
De las yerbas y las flores,
Y de mortales engaños,
Y de sublimas dolores
4
Yo he visto en la noche oscura
Llover sobre mi cabeza
Los rayos de lumbre pura
De la divina belleza.

and completed in 18 verses.

http://jose-marti.org/jose_marti/obras/poesia/versossencillos/03yosoyunhombresincero.htm

In a four-part article, La guantanamera por Maria Argelia Vizcaino, she discusses the origins of the song, first broadcast in 1930 on a Habana radio station, a creation of Joseíto Fernández.