WILLIAM H. OSLER was born in New Jersey in June of 1841 to Samuel and Abigail Osler. The family was living in Camden's Middle Ward in 1850, according to that year's census. The 1860 Census shows the family living in Camden's Middle Ward. There were six children at home, ranging in ages from 4 to 18, William being the oldest, followed by Anne, John, Sarah, Kate, and Abigail. Samuel Osler's occupation is given as "fireman of engine" and the oldest son, William worked as a "slip tender", they both may have been working aboard one of the ferries.  

William H. Osler was appointed to the Camden Fire Department to replace George B. Glover, who had resigned as an extra man with Engine Company 2 on May 21, 1871. William Osler was had been an engineer, that is, as an operator of a steam engine, a necessary skill as steam engines were mounted on the horse-drawn apparatus of the day in order to provide pressure to the hoses utilized in extinguishing fires, prior to joining the Fire Department. When William J. Ross, the engineer of Engine Company 2, resigned on June 8, 1871, William Osler was promoted to take his place 12 days later. He served in that capacity into 1872, but appears to have left the department when Henry F. Surault was Chief Engineer during 1872 and 1873, when Chief Robert S. Bender had taken a leave of absence. William H. Osler was again serving as an extra man with Engine Company 2 in late 1873, and was again promoted to Engineer on February 5, 1874. William Osler was again called to service, on June 1, 1878, as an extra man with of Hook & Ladder Company, when John Chew resigned. William H. Osler served until April of 1882, when Samuel Welsh was appointed in his place.

William H. Osler was living at 424 Taylor Avenue when he joined the department  and during the early 1870s. He was living at 426 South 3rd Street in the spring of 1879. When the census was taken in 1880 he was living on South 2nd Street with his wife Rebecca and sons Thomas, George H., and Samuel Osler. His next door neighbor was John Vanstavern, who had also served with the Camden Fire Department for  time.

The 1900 Census shows that William H. Osler was living at 408 South 5th Street, the home of his niece Ida and her husband William Godfrey. William H. Osler's brother John and his mother Abigail also lived at the South 5th Street address.

Willim H. Osler died on May 11, 1907 at the age of 65. Services were held at the home of his son Thomas F. Osler, 2015 Fillmore Street in Camden. William H. Osler was buried at Evergreen Cemetery in Camden.