Millini was born on 4 July 1644 to Mario and his wife Ginevra (née di Neri Capponi).

He was a great-nephew of Cardinal Giovanni Garsia and both his parents were members of families of the Roman civic nobility.

His family and three brothers all fought in the papal armies.

In the same year he was nominated Papal nuncio to Madrid.

This article about an Italian Catholic cardinal is a stub.