Frederick was the son of the prominent London decorator John C. Crace (1754–1819), who had been hired in 1788 to provide Chinese works of art for the Royal Pavilion.
Frederick married Augusta Harrop Gregory, the daughter of John Gregory, a London magistrate and treasurer of the Whig Club. In 1830 his son John Gregory became a full partner in the family business, thereafter known as Frederick Crace & Son, in 1830, on inheriting property and capital from his mother, who had died in 1827. Crace & Son designed the St James's Theatre, London (1835) and the younger Crace developed into a well-regarded designer of theatres on his own.
For Crace's collection of topographical prints and drawings, Thomas H. Shepherd was employed to paint old London buildings prior to their demolition, to provide a historical record.
He died at his home in Hammersmith on 18 September 1859, aged 80, and was buried at West Norwood Cemetery. His extensive collection was purchased for the British Museum in 1880.