He was born in April 1795 in Long Benton, nearby to the northeast of Newcastle upon Tyne, the son of Joseph Addison, who was a grocer and flour dealer there.

His thesis was on Dissertatio medica inauguralis quaedam de syphilide et hydrargyro complectens (Concerning Syphilis and Mercury).

Guy's Medical School recorded his entrance as follows: "Dec. 13, 1817, from Edinburgh, T. Addison, M.D., paid pounds 22-1s to be a perpetual Physician's pupil."

He was promoted to assistant physician, with the support of Benjamin Harrison, in January 1824 and in 1827 he was appointed lecturer of materia medica.

As well, Addison worked under Thomas Bateman, a dermatologist, at the General or Public Dispensary on Carey Street, Holborn.

[1] In 1837, Addison became joint lecturer with Richard Bright on practical medicine, and a full physician at Guy's Hospital.

[1] In 1860 he wrote to his medical students as follows: "A considerable breakdown in my health has scared me from the anxieties, responsibilities, and excitement of my profession."

The day after his death, the Brighton Herald recorded that: "Dr Addison, formerly a physician to Guy's Hospital, committed suicide by jumping down the area (i.e. the space between the front of the house and the street) of 15 Wellington Villas, where he had for some time been residing, under the care of two attendants, having before attempted self-destruction.

It is a type of megaloblastic anemia, in which a lack of intrinsic factor causes absorption of vitamin B12 to be impaired.

[1] In the classification of skin diseases by morphology, and their diagnosis, he was a follower of Robert Willan and his own teacher Thomas Bateman.

[15] In 1847 Addison married at Lanercost Priory Elizabeth Catherine Hauxwell, a widow, with two children from her first marriage.