TL;DR: Both are correct.
The word élite (or elite) is a loan word from French élite. It means:
Del fr. élite.
- f. Minoría selecta o rectora.
The trick is that the é in French does not mean that the first e is stressed, it only indicates the proper way of pronouncing it (/e/ vs /ɛ/). So in French it is pronounced (roughly) as [elít].
You can read this in the Diccionario panhispánico de dudas:
The French word élite [...] was adapted to Spanish as elite [elíte]; but the original word élite also circulated a certain time unchanged from French, so people who did not know French pronounced it the Spanish way: [élite]. Although this pronunciation goes against its etymology, it is today the most common way of writing this word [...]. Thus, the élite form and its pronunciation are also considered valid.
So in the end both ways ended up being accepted by the RAE, although the form élite was not accepted until very recently (2001 while elite was included in 1984).
This is the first match in CORDE:
En Europa, donde las grandes masas de tropa están en columna y el campo de batalla abraza aldeas y villas diversas, las tropas de élite quedan en las reservas para acudir a donde la necesidad las requiera.
Domingo Faustino Sarmiento, "Facundo. Civilización y barbarie", 1845-1874 (Argentina).