Alberti was born in Amsterdam as the third of eight children to Jacobus Wilhelm Verbrugge and Sophia Jacoba van Musscher.
In 1944 he married Ria Kuiper, and his daughter Willeke Alberti, later to become a successful Dutch vocalist herself, was born in 1945.
In the 1960s he began to act alongside his daughter Willeke; as a duo, they also scored hits on the Dutch charts.
From 1965 father and daughter presented a popular monthly television show for the AVRO.
In 1984, Alberti was diagnosed with liver cancer, and he died in Amsterdam on 18 February of the following year, aged 58.