In 1419, Giovanni di Bicci de' Medici offered to finance a new church to replace an eleventh-century Romanesque rebuilding.

Filippo Brunelleschi, the leading Renaissance architect of the first half of the fifteenth century, was commissioned to design it, but the building, with alterations, was not completed until after his death.

The church is part of a larger monastic complex that contains other important architectural and artistic works: the Old Sacristy ("Sagresta Vecchia") by Brunelleschi and having interior decoration and sculpture by Donatello; the Laurentian Library by Michelangelo; the Medici Chapels, two structures that include the New Sacristy ("Sagrestia Nuova") based on Michelangelo's designs; and the larger Cappella dei Principi ("Chapel of the Princes") being a collaboration between the family and architects.

Although the building was largely completed by 1459 in time for a visit to Florence by Pius II, the chapels along the right-hand aisles were still under construction during the 1480s and 1490s.

"[3] At times, the design of San Lorenzo has met with criticism, particularly when compared with Santo Spirito, also in Florence and which is considered to have been constructed more or less in conformity with Brunelleschi's ideas, even though he died before most of it was built.

The Medici Pope Leo X gave Michelangelo the commission to design an outer façade of the basilica in white Carrara marble in 1518.

In recent years, the association of "Friends of the Elettrice Palatina" and the Comune of Florence re-visited the question of completing the outer facade of the basilica according to Michelangelo's designs.

That the architect of a building also designed the interior furnishings is a historical novelty in European architecture that is driven by his being a sculptor by training.

Michelangelo completed most of the statuary for the new sacristy as well, however, the statues of the two patron saints planned to accompany the Madonna and Child that were planned for placement on the main wall and the sculptural elements of the two sarcophagi were left undone when he was redirected to another project by the pope, the political situation in Florence changed, and changes later occurred in papal succession.

[7] In a statement in a biography of Michelangelo that was published in 1553 by his disciple, Ascanio Condivi, and reportedly is based largely on Michelangelo's own recollections, Condivi gives the following description of the sculptures that were planned for the sarcophagi: The statues are four in number, placed in a sacristy... the sarcophagi are placed before the side walls, and on the lids of each there recline two big figures, larger than life, to wit, a man and a woman; they signify Day and Night and, in conjunction, Time which devours all things... And in order to signify Time he planned to make a mouse, having left a bit of marble upon the work (which [plan] he subsequently did not carry out because he was prevented by circumstances), because this little animal ceaselessly gnaws and consumes just as time devours everything.

Above is the Cappella dei Principi (Chapel of the Princes), a great but awkwardly domed octagonal hall where the grand dukes are buried.

The Corbelli chapel, in the southern transept, contains a monument by the sculptor Giovanni Dupré to the wife of Count Moltke-Hvitfeldt, formerly Danish ambassador to the Court of Naples.