Well this is nice, a question that is actually about my home country, city, and about my family! You see, my father is a bandoneonist, so tango has been a key part of my life for as long as I can remember. I will translate every name, mainly song titles and sources, because said sources don’t tend to be translated to English, as far as I’m aware.

Origins

How tango originated as a genre is a matter of some debate amongst Argentine musicologists and historians, mainly because of its context of origin: slums. It was born in Buenos Aires, that much is known, and it spread to Montevideo (Uruguay) over the next decade following its birth.

The oldest tangos still played today are called “Cara Sucia”, or “Dirty Face”, an extremely pornographic song, written in 1884 by Afro-Argentine violinist Casimiro “el Negro” Alcorta, and “El Entrerriano”, meaning “The Entrerrian”, or “The Man from Entre Ríos” (Entre Ríos is a province North of Buenos Aires). It was composed by Rosendo Mendizábal, a pianist, who premiered the song around 1897, according to Héctor and Luis Bates’ La Historia del Tango (Tango’s History).

However, before tango, existed something we now call paleo-tango or proto-tango, which, as you say, was indeed born from a cultural exchange between African Argentines and orilleros, or waterfront people, who were essentially stevedores, or simply people who lived in the slums surrounding Buenos Aires’ port. However, there was a third cultural group that participated in this exchange: immigrants. During the final years of the XIX century, many Europeans immigrated to Argentina, under the presidencies of Domingo Faustino Sarmiento and later Julio Argentino Roca. Their plan was to encourage a sort of “enlightened” European immigration, seeking to attract the upper echelons of society towards our shores. However, the result was mostly lower class, proletarian Europeans, particularly Italians and Eastern Europeans. For the purposes of this answer I will include Germany in Eastern Europe.

This exchange gave birth to a peculiar musical mixture of Argentine rhythms and Spanish dialect; African percussionism-based music; Romani dances and instruments; Italian dances; and a key element, mythically introduced to Argentina by German sailors: the bandoneon. This very peculiar, German born instrument, which, in spite of its appearance isn’t particularly similar to an accordion, is considerably more akin to a regular church organ, became the essence of bandoneon, because it’s ability to produce both extremely low sounds with the left hand, and remarkably high ones with the right, was capable of replacing the traditional percussion instruments, while also maintaining the traditional flair that characterises Romani/Gypsy dances.

Now, tango emerged as a deeply lower class form of cultural expression. As a dance, it was mostly performed in the streets, in pulperías, pubs that resemble the archetype of Wild West saloons, and brothels. As such, it was heavily associated with sex workers, proletarian workers, and the abuse of alcohol. Early attempts to introduce it as a formal dance form were not very well received, as stated by a complaint filed in 1873 to the Municipal Corporation of Buenos Aires, regarding a dance academy belonging to one Carmen Gómez, citing "se cobra entrada y se espende bebidas espirituosas, por cuyo efecto resultan escándalos a deshoras de la noche", which translates to “an entrance fee is charged and spirit beverages, which causes scandals late at night” and “"por la clase de gente que en ella se reune", “due to the kind of people that gathers there”.

Having said this, I’d like to note that tango doesn’t exactly originate from a specific musical influence, but instead, it takes many different elements from a diverse array of genres, such as tango andaluz (a variant of flamenco), milonga, habanera, payada and waltz. As an amalgam, it developed its own identity, with several mythologised figures such as El Cachafaz, one of the most famous tango dancers in history (his real name was Ovidio Bianquet), and its very own argot, lunfardo, which is as complex as any dialect, but doesn’t qualify as one. Lunfardo derives from many languages, primarily Spanish, Italian and Quechua, and it’s prevalent in most tango lyrics. Some lunfardo words are actually use everyday in Argentine Spanish! I use many of them quite frequently.

Rising fame

Mendizábal was one of the people responsible, together with El Cachafaz, of the gradual popularization of tango, particularly during the early 1910s, the two of them belonging to an artistic movement known as La Guardia Vieja, or The Old Guard, a group of tango musicians who sought to take the genre away from the slums and into the world.

Even if the upper classes detested it, tango was exported to Europe, mainly due to its very antagonistic dance style: close proximity, very touchy feely (pardon my very academic words), and overall, very sexually charged. In Recepción del tango rioplatense en Italia (The reception of Río de la Plata’s tango in Italy), Enrique Cámara de Landa explains that in early 1914, Kaiser Wilhelm II expressly forbade Prussian officers from dancing tango when in uniform. The decission was applauded by Vatican newspaper L’Osservatore Romano, which printed an editorial that stated “The Kaiser has done what he could to avoid gentlemen from identifying themselves with the lowly sensuality of blacks and half bloods (...) And some go around claiming that tango is a dance like any other, when it is not danced licentiously! This dance tango is, at the very least, one of those that cannot, under any circumstances, be kept with any probability of decency. Because, if in any dance, the morality of dancers is in certain danger, in tango, decency has sunk, and for this reason, emperor Wilhelm has forbidden this dance to officers wearing their uniforms.”

However, the most influential figure in La Guardia Vieja, and certainly one of the most famous figures in the history of tango, was Carlos Gardel. A legend, a myth, but certainly a man, his short but spectacular career has been the subject of many investigations, biographies, songs, movies and so forth. While there’s still a bit of debate on the matter, he was almost certainly born in Toulouse around 1890. However, he was raised in Buenos Aires, where he became enamoured with tango, turning into one of the most important singers in Latin American history. From the late 1910s until his death in 1935, his popularity grew exponentially, and with his, so did tango’s. He began touring Latin América, then Europe and the US. His voice, as well as his acting capabilities, allowed him to become one of the biggest stars ever to emerge from Argentina. He filmed eleven movies, ten of them produced by Paramount, including El Día Que Me Quieras, The Day That You Will Love Me, directed by John Reinhardt, filmed in New York, where he met a very young Astor Piazzolla, and The Big Broadcast of 1936 (1936), where he appeared together with Bing Crosby, Bill Robinson, the Ray Noble Orchestra and Glenn Miller.

His singing and acting career, paired with his sudden death in a plane accident in Medellín in 1935, helped increase international interest in tango as a genre, and, much as it was the case with jazz, tango had a transformation, from the music of the oppressed and the poor, to the preferred cultural expression of the upper classes both in Argentina and in many other countries during the 30s and 40s.