Storck was baptized in the Noorderkerk, a Protestant church in the Jordaan. His father was the painter Jan Jansz Sturck (or Johannes Storck) (1603-1673), from Wesel; his mother was Teuntje (Apolonia) Jacobs. The couple married in 1628. Storck had two brothers, who were also painters using the name Sturckenburch until c. 1688 after which they started calling themselves Storck or Sturck. It is likely they were all trained with their father in the family workshop and joined the local Guild of Saint Luke, otherwise it was impossible to sell any painting.
Around 1666 Storck set up his own workshop producing naval, harbor scenes as well as landscape paintings and city scapes. In 1670 he traveled with his brother Jacob and worked in Germany. In 1694, being 49 years old, he married the widow Neeltje Pieters van Meyservelt. At the end of his life he lived on Kattenburg near the harbour.