Mew IS actually the 150th Pokemon.
Its Pokedex entry says 151 because MewTwo was discovered (at large)first but MewTwo is simply a failed clone of Mew's DNA which Giovanni and his thugs actually discovered BEFORE they created Mewtwo.. Hence the name (Mew Two ).
The Pokémon are listed by when they're discovered, not when they first existed, though... That's why Pokémon have different numbers in different regions, because they were discovered sooner in some areas and later in others.
For example, Arcanine is #059 in Kanto, because it was the 59th Pokémon discovered in Kanto, whereas it's #130 in Jhoto, #052 in Unova, and #053 in Alola.
[Arcanine's Bulbapedia Article]
[Bulbapedia's Artilce on New/Old Pokédexes]
So by your very own statement, due to "MewTwo was discovered (at large)first", that means that in Kanto, he would have a number that comes before Mew's, though in another region where Mew might be discovered first, it's number would come before MewTwo's.