Galileo was born in Pisa (then part of the Duchy of Florence), Italy in 1564, the first of six children of Vincenzo Galilei, a famous lutenist, composer, and music theorist; and Giulia Ammannati. Galileo became an accomplished lutenist himself and would have learned early from his father a healthy scepticism for established authority,the value of well-measured or quantified experimentation, an appreciation for a periodic or musical measure of time or rhythm, as well as the illuminative progeny to expect from a marriage of mathematics and experiment. Three of Galileo's five siblings survived infancy, and the youngest Michelangelo (or Michelagnolo) also became a noted lutenist and composer, although he contributed to financial burdens during Galileo's young adulthood. Michelangelo was incapable of contributing his fair share for their father's promised dowries to their brothers-in-law, who would later attempt to seek legal remedies for payments due. Michelangelo would also occasionally have to borrow funds from Galileo for support of his musical endeavours and excursions.

These financial burdens may have contributed to Galileo's early fire to develop inventions that would bring him additional income.

Galileo was named after an ancestor, Galileo Bonaiuti, a physician, university teacher and politician who lived in Florence from 1370 to 1450; at that time in the late 14th century, the family's surname shifted from Bonaiuti (or Buonaiuti) to Galilei. Galileo Bonaiuti was buried in the same church, the Basilica of Santa Croce in Florence, where about 200 years later his more famous descendant Galileo Galilei was also buried. When Galileo Galilei was 8, his family moved to Florence, but he was left with Jacopo Borghini for two years.

He then was educated in the Camaldolese Monastery at Vallombrosa, 35 km southeast of Florence.[

Although a genuinely pious Roman Catholic, Galileo fathered three children out of wedlock with Marina Gamba. They had two daughters, Virginia in 1600 and Livia in 1601, and one son, Vincenzo, in 160.] Because of their illegitimate birth, their father considered the girls unmarriageable, if not posing problems of prohibitively expensive support or dowries, which would have been similar to Galileo's previous extensive financial problems with two of his sisters.Their only worthy alternative was the religious life. Both girls were accepted by the convent of San Matteo in Arcetri and remained there for the rest of their lives.[
Virginia took the name Maria Celeste upon entering the convent. She died on 2 April 1634, and is buried with Galileo at the Basilica of Santa Croce, Florence. Livia took the name Sister Arcangela and was ill for most of her life. Vincenzo was later legitimised as the legal heir of Galileo, and married Sestilia Bocchineri.