Drexel and Company was founded as a currency brokerage in 1838 by Francis Martin Drexel (1792-1863). The first office in Philadelphia was located at 34 South Third Street. Francis Martin Drexel's sons Anthony Joseph Drexel and Francis Anthony Drexel became partners of the private banking firm in 1847, and their younger brother Joseph Wilhelm Drexel became a partner soon after. In 1851, the company earned large profits from gold discoveries in California when Francis Martin Drexel opened up a banking house, Drexel, Sather and Church, in San Francisco.

During the Mexican-American War (1846-1848), Drexel and Co. sold $49.2 million of the U.S. Treasury's war bonds. The firm was again involved in bond sales for the federal government during the U.S. Civil War. In partnership with Jay Cooke's firm, Drexel and Co. began the new practice of purchasing Treasury bonds from the federal government and selling the bonds to ordinary citizens. Jay Cooke's salesmanship, which relied on patriotic feeling in the Union as the Army was suffering losses, was bolstered by the stability of Drexel and Co. The partnership continued until 1864, at which point the total from bond sales was near $511 million. The incredible success of bond sales sustained the Union's ability to fund its military during the Civil War.

Anthony J. Drexel became the de facto head of Drexel and Co. after the death of Francis M. Drexel in 1863. Over the next two decades, Drexel and Co. became heavily involved in financing the railroad industry through clients Pennsylvania Railroad, Lehigh Coal and Navigation Co., and the North Missouri Railroad. J. Pierpont Morgan agreed to become the head of Drexel and Co.'s New York firm, which would be renamed Drexel, Morgan, and Co. The branch opened in July 1871. As Morgan gained prominence for his business dealings, Anthony Drexel was his constant counsel and mentor. In late 1894, after the death of Anthony J. Drexel in June 1893, J. Pierpont Morgan gathered all of the partners of the New York and Philadelphia banking houses and shared his plan for reorganization. The two houses were combined, based out of New York, and renamed J.P. Morgan and Co. The Paris branch became Morgan, Harjes and Co. Only the Philadelphia branch retained the Drexel name.

Construction on a new banking house began in 1885 on the southeast corner of Fifth and Chestnut Streets. A second Drexel Building was established on the same block in 1888. The building was the tallest in the city at the time at eleven stories, and essentially forced the movement of the Third Street financial district into this block. In 1927, a building designed by Day and Klauder, architects, in an Italian Renaissance palazzo manner was constructed at 43 S. 15th Street in Philadelphia. Drexel and Co. occupied the building until 1943.

By 1940, the historic Drexel and Co. was entirely absorbed into the J.P. Morgan and Company commercial bank. That year, several former Drexel partners and associates re-established Drexel and Co. as an investment bank. In 1965, the new firm merged with Harriman, Ripley and Company to become Drexel Harriman Ripley. In the early 1970s, Drexel Harriman Ripley sold a 25 percent stake to Firestone Tire and Rubber Company, and was renamed Drexel Firestone. After a merger with Burnham, the name changed to Drexel Burnham and Company. Finally, in 1976 the group merged with Lambert Brussels Witter to become Drexel Burnham Lambert Group Inc.