Cullen was born in Tenerife, Canary Islands, but moved to Argentina in the 1820s after establishing commercial activities (linked with fluvial trade) in the area.

After being involved in activism related to the independence of Uruguay and the resistance against Brazil (see Cisplatine War), he returned to Santa Fe, settled in a ranch, and married Joaquina Rodríguez del Fresno, the young widow of Pedro Aldao and sister-in-law of López.

However, right after crossing the Arroyo del Medio and entering the territory of Buenos Aires Province, his captors announced they had orders to kill him.

Cullen was assisted by a priest in San Nicolás de los Arroyos and wrote a letter to his wife; he was then killed by a firing squad, on 21 June 1839.

Cullen emigrated to the Río de la Plata region, first settling in Montevideo, Uruguay, in 1811, and moving then to Santa Fe in 1823.