Van Aelst was born in Delft to a family of prominent city magistrates. He studied to paint from his uncle, the still-life painter Evert van Aelst. On 9 November 1643 he enrolled as a master of the Guild of Saint Luke at Delft.

from 1645 to 1649 he lived in France. In 1649 Van Aelst went to Florence, where he worked as court painter to Ferdinando II de' Medici, grand duke of Tuscany. Here he was known as Guillielmo d'Olanda. At the same time, the grand duke also employed two fellow Dutchmen Matthias Withoos and Otto Marseus van Schrieck, the latter also a still-life painter who influenced Van Aelst's style. Ferdinando II publicly presented Van Aelst with a gold chain and medal, as a testimony of his approbation and an acknowledgment of his talents.

It's been conjectured that van aelst visited rome where he became a member of the bentvueghels, an affiliation of in particular dutch and flemish artists active in rome. This conjecture is based totally, now not very convincingly, on his exercise at some point of the years 1657/58 to sign his works with his call followed through: ‘alias (and a drawn stick determine)'. Some interpreted this as a connection with a unethical call (the nickname that a member of the bentvueghels would adopt) – de vogelverschrikker (dutch for 'scarecrow')- however there are no documents confirming this.

In 1656 he came back to the Netherlands to settle permanently in Amsterdam. He became one of the most prominent still-life painters of his generation, which allowed him to live on the Prinsengracht. He must have at Amsterdam died in 1683 or shortly thereafter, as his latest dated work is from that year. Van Aelst taught Rachel Ruysch, Isaac Denies, Maria van Oosterwijck, and Ernst Stuven.