Edit: With the release of The Cursed Child comes new answers! The current headmistress is Minerva McGonagall
But I was advised when I took this job
The Cursed Child, page 132
In an interview JKR said that
J.K. said that "McGonagall was really getting on a bit," and nineteen years after the Battle of Hogwarts, there is an entirely new headmaster. Also, there is a new Defense Against the Dark Arts teacher, and that position is now as safe as the other teaching posts at Hogwarts, since Voldemort's death broke the jinx that kept a Defense Against the Dark Arts professor from remaining for more than a year
This is 19 years after the battle of hogwarts though, It is more than safe to assume that McGonagall was the immediate acting Headmistress of Hogwarts after the battle. Considering she was Deputy before Dumbledore died and Headmistress for a short while before Voldemort placed Snape in command.
There are two different parts of the Lexicon which say McGonagall was the headmistress until an unknown date.
Headmistress 1998 ff.
Head of Gryffindor House
On staff since December of 1956 (OP)
And on a list of Headmasters she is at the bottom:
Minerva McGonagall (1998 -?)
I believe that McGonagall was definitely head for a number of years whilst she got Hogwarts back in order until like JKR said she got on a bit. The earliest we can state this as for definite would be 2014/15. She could have been in office for anywhere between 1 month - 19 years but she was definitely the acting headmistress after the battle.