The Bellini was invented sometime between 1934 and 1948 by Giuseppe Cipriani, founder of Harry's Bar in Venice, Italy. He named the drink the Bellini after the 15th-century Venetian artist Giovanni Bellini. The drink started as a seasonal specialty at Harry's Bar and it became a year-round favorite in the whole world.

The basis for the drink are fresh vineyard peaches. They appear in various shapes like the saturn peach and are harvested in late spring through the end of summer. The inside of the peach is pale in appearance. Hence, the perfect shade of color of a Bellini should be peach white with slight glimpse of pink.
For the purée just peel the peach and get rid of the stone.
Afterwards mix all the peaches and if necessary add some cane sugar sirup. Done!
-- BELLINI --
After a recipe for „Harry’s Bar“
3cl white peach purée
10 cl Prosecco or Champagne
Just take a champagne glas, add the white purée as well as half of the champagne and gently stir. Add the rest of the sparkling vine until the glas is full and gently stir again.
Photo credit:
http://chilledmagazine.com/bella-bellini-modern-recipes-for-a-classic-cocktail
http://mixology.eu/klassik/der-bellini-cocktail-venedig/