Joseph Bradley was born in Berne, New York, on March 14, 1813. He adopted the middle initial "P" as a young man, although the initial did not stand for anything. After growing up in a farm family, he decided to move to New York City when he was 18 years old. Nevertheless, he was stranded in Albany because of unfavorable weather, and spent a few days listening to debates in the state legislature. This event changed the course of his life; later, Bradley explained that, had his trip not been interrupted, he "would have become a grocer in New York." Encouraged by a former teacher, he obtained admission to Rutgers College, New Jersey in 1833. After graduating, he began an intense independent study of law, and passed the bar in 1839. He practiced law for 30 years in Newark, New Jersey, specializing in patent, commercial and railroad law. In addition, he worked as a legislative correspondent and an actuary for an Mutual Benefit Life Insurance. He married Mary Hornblower in 1844, and the couple had seven children together.
The Republican Bradley made an unsuccessful bid for Congress in 1862. In 1870, President Ulysses S. Grant nominated him to the US Supreme Court. Although he had no judicial experience, Bradley was at the top of his profession as an attorney and was able to martial support from a number of politicians. He was confirmed by the Senate on March 21, 1870. A year later, he helped reverse the legal tender decision, thus permitting debts incurred after 1862 to be paid in paper money rather than only gold or silver.
Bradley contributed a brilliant mind and broad knowledge of the law to the Court. He was an eccentric man with "little or no deference for the mere opinion of others." While he was greatly influential in his understanding of commercial law; other areas, such as civil rights, confounded him, unable as he was to see beyond the racial and gender prejudices of his time.
In 1877, while on the Court, Bradley was appointed to the electoral commission to decide the result of the 1876 presidential election, which was under dispute. The commission, divided along partisan lines, declared Rutherford B. Hayes President by one vote.
Bradley died on January 22, 1892, while still serving on the Court.