Albrici was born as the son of singer who settled from Marche in Rome. In 1641 he became a student at the Collegium Germanicum et Hungaricum under Giacomo Carissimi. In 1647 he was paid as an organist in the Santa Maria in Vallicella. In 1652 he was invited by Alessandro Cecconi and started to work for Queen Christina of Sweden together with his brother, who joined the boys' choir. His father, an alto, sang the Lord's Prayer in Swedish when the Queen abdicated in June 1654. Albrici stayed in Stockholm when Karl X Gustav became king.
Vincenzo and his sister Leonora, also a singer, went to England and became part of the King's Italian Musicke. Bartolomeo joined them in 1666 and remained in England  when Vincenzo returned to Dresden. In 1681 he gained the post of organist at the Thomaskirche, a position which required conversion to Protestantism. After a few months already he moved to the Augustine church of St. Thomas, in Mala Strana, Prague for the rest of his life.
Works, editions and recordings
- Concerti Sacri a 1, 2, 3 voci con strumenti, Cappella Augustana Matteo Messori. Label: Musica Rediviva.