Born in Venice, Marcello was the son of a senator. As such, he enjoyed a comfortable life that gave him the scope to pursue his interest in music. He was a contemporary of Tomaso Albinoni. He held concerts in his hometown and also composed and published several sets of concertos, including six concertos under the title of La Cetra (The Lyre), as well as cantatas, arias, canzonets, and violin sonatas. Marcello, being a slightly older contemporary of Antonio Vivaldi, often composed under the pseudonym Eterio Stinfalico, his name as a member of the celebrated Arcadian Academy (Pontificia Accademia degli Arcadi). He died in Padua in 1747.
Alessandro's brother was the more well-known Benedetto Marcello, also a composer, who illegally married his singing student Rosanna Scalfi in 1728. After his death she was unable to inherit his estate, and in 1742 she filed suit against Alessandro Marcello, seeking financial support.
Although most of his works are infrequently performed today, Marcello is regarded as a very competent composer. His La Cetra concertos are "unusual for their wind solo parts, concision and use of counterpoint within a broadly Vivaldian style," according to Grove, "placing them as a last outpost of the classic Venetian Baroque concerto."
The Concerto for Oboe and Strings in D minor op. 1 is perhaps his best-known work. Its worth was affirmed by Johann Sebastian Bach who transcribed it for harpsichord (BWV 974). A number of editions have been published, including an edition in C minor because the baroque oboe played a whole tone lower than the modern oboe.