I think it's an evolution such as takes place in any language in different ways. In English, I suspect this particular one comes from the mix of different other-language speakers learning English and the habit has spread because of modern media diffusion.
It is interstingly not a complete evolution. With two prepositions involved, it was originally 'tell it to me', just as it still is 'explain it to me'. The incompleteness can be felt/seen if you say something like 'I told him it'. There's a slightly clumsy feel, to me at least, in the use of the two pronouns side by side.
Consider also that English is unusual in having two words for what is often only one in other languages - to say and to tell, for dire in French. You wouldn't say 'Say it me' or 'Say me it'. Equally, the indirect object//dative case form applies to speak/talk//parler. 'Speak French to him', or 'talk sense to me' are the ways we say it. Not 'talk me sense' or 'speak him French'. So it is 'tell' that seems to have undergone this semi-evolution, why I cannot be sure. Or really I haven't a clue. But it doesn't have nowt to do with Latin vs Germanic etymology.