Jatta, 54, steps up from her current role as deputy director on January 1st, taking over from Antonio Paolucci, 77, an art historian and former Italian culture minister.
Jatta, a native of Rome, has worked at the Vatican since 1996. She will be taking over one of the world's greatest collections of artworks, contained in seven kilometres (four miles) of galleries and including the celebrated Sistine Chapel.
The museums draw in four million visitors each year despite a relatively hefty standard adult entry price of 16 euros ($16.60).
Most reviews are highly favourable despite some grumbling that the visitor experience is negatively affected by overcrowding.