Born in Navesink, New Jersey, Strickland's father was a master carpenter and a member of the Practical House Carpenters' Society. Strickland's father worked on the Bank of Pennsylvania which brought his son William to the attention of Benjamin Latrobe, the architect of the bank. William apprenticed with Latrobe for two years until he left to try his hand at painting.
In 1815 he submitted a design for the Second Bank of the United States which instantly thrust him to the van of the architectural profession. The Second Bank, modeled on the Greek Parthenon, was one of the first Greek Revival buildings in the United States, and led to other commissions.
Active in social and cultural affairs, Strickland was a member of the American Philosophical Society, the Franklin Institute, and the Musical Fund Society.
Despite his reputation, he lost the prestigious competitions to design Girard College to ex-student Thomas U. Walter; Laurel Hill Cemetery and the Philadelphia Athenaeum to John Notman; and the Franklin Institute to John Haviland.
In 1837, a financial panic in Philadelphia curtailed all commissions, causing Strickland to head south. He died during the construction of his last major work, the State House in Nashville, Tennessee. He is entombed beneath that building, which today is featured on Tennessee license plates.