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He was born in Yeniseysk, Russia, in 1863, as the son of the physician Adam Onufrowicz and Maria. He attended Industrieschule Zürich and later studied medicine at the Zurich University. He was a pupil of August Forel. Circa 1890 he emigrated to USA. He worked in Pathological Institute of NY State Hospitals under the directorship of Ira Van Gieson and later became lecturer in NY Polyclinic. From 1899, he worked in St. Catherine Hospital, NY. Later he practised in Craig Colony for Epileptics in Sonyea, NY. In the 1920s, he was a consulting neurologist at U.S. Marine Hospital 43, located on Ellis Island. He was a member and vice-president of New York Psychoanalytic Society, member of American Neurological Association (since 1895), secretary and vice-president of the New York Neurological Society.
- Forel A, Onufrowicz B. Weitere Mitth. ueber den Ursprung des Nervus acusticus. Neurologisches Centralblatt 9, 193 (1885)
- Onufrowicz, Br. (1885). "Experimenteller Beitrag zur Kenntniss des Ursprungs des Nervus acusticus des Kaninchens". Archiv für Psychiatrie und Nervenkrankheiten. 16 (3): 711–742. doi:10.1007/BF02057570.
- A Method of Securing Fixation and Hardening of the Central Nervous System Before the Autopsy. 1887
- The Warding-Off Neurop Psychoses. The Journal of Nervous and Mental Disease (1894)
- Onuf (Onufrowicz) B. The Biological and Morphological Constitution of Ganglionic Cells, as Influenced by Section of the Spinal Nerve Roots of Spinal Nerves. The Journal of Nervous and Mental Disease 20, 10, 597 (1895) 
- Onuf (Onufrowicz) B. A Study in Aphasia. Journal of Nervous & Mental Disease 24, 2, 86-97 (1897) 
- The Manner in which the Law Forbidding the Public Representations of Hypnotism ought to be Modified. Journal of Nervous & Mental Disease 24(12):782 (1897)
- Onuf. DUBOISINE SULPHATE IN THE TREATMENT OF PARALYSIS AGITANS. Journal of Nervous & Mental Disease 24(7):448 (1897)
- ON SENILE EPILEPSY AND GRIESINGER'S SYMPTOM DUE TO BASILAR THROMBOSIS. Journal of Nervous & Mental Disease. 24(7):439 (1897)
- NEUROPATHOLOGY: A CASE OF LESION OF THE TRACTUS OPTICUS AND OF THE PEDUNCLE. Journal of Nervous & Mental Disease. 24(7):434 (1897)
- Onuf B, Collins J. Experimental Researches on the Localisation of the Symphatethic Nerve in the Spinal Cord and Brain, and contribution to its Physiology. The Journal of Nervous and Mental Disease 25, 9, 661 (1898) 
- Notes on the Arrangement and Function of the Cell Groups in the Sacral Region of the Spinal Cord. Journal of Nervous & Mental Disease 26(8):498-504 (1899) 
- On the arrangement and function of the cell groups of the sacral region of the spinal cord in man. Arch Neurol Psychopathol (1900)
- Onuf B, Collins J. EXPERIMENTAL RESEARCHES ON THE LOCALIZATION OF THE SYMPATHETIC NERVE IN THE SPINAL CORD AND BRAIN, AND CONTRIBUTIONS TO ITS PHYSIOLOGY. Arch Neurot Psychopath 3, 3 (1900) 
- The differential diagnosis of multiple sclerosis. Brooklyn Medical journal 16, 483-487, 1902
- Reference Hand-Book of Medical Sciences (1903)
- Pilcher, LS; Onuf, B (1903). "VI. Perforating Gunshot Wound of the Cervical Portion of the Spinal Cord. Report of a Case in which Recovery was secured, with Ability to Walk". Annals of Surgery. 38 (6): 812–24. PMC . PMID 17861394.
- Onuf B. Note on a Stain applicable to Differential Leucocyte Counts in the Counting Chamber. J Med Res 12(1): 87–93 (1904) PDF
- Onuf (Onufrowicz) B. On the Association of Epilepsy with Muscular Conditions Fitting Best into the Cadre of the Myopathies. Trans Amer Neurol Assoc 31, 240-255 (1905)
- Onuf B, Lograsso H. Researches on the Blood of Epileptics. Amer J Med Sci 131, 269-285 (1906)
- Onuf (Onufrowicz). ON THE ASSOCIATION OF EPILEPSY WITH MUSCULAR CONDITIONS FITTING BEST INTO THE CADRE OF THE MYOPATHIES. Journal of Nervous & Mental Disease. 33(1):13-28 (1906)
- Onuf B. DEMONSTRATION OF A NEW METHOD OF BRAIN RECONSTRUCTION. Journal of Nervous & Mental Disease. 35(11):712 (1907), 35(2):712
- Onuf B. DREAMS AND THEIR INTERPRETATION AS DIAGNOSTIC AND THERAPEUTIC AIDS IN PSYCHOPATHOLOGY Journal of Nervous & Mental Disease. 37(1):47 (1910) 
- Onuf B. Some Features of the Epileptic Attack. New York Med J 78, 871 (1913)
- On the Role of Masturbation, Especially as Applied to Some Psychoses. Urologic and Cutaneous Review 21, 10, 562-70 (1917)
- Onuf-Onufrowicz, Bronislaw (1920). "Frederick Chopin's Mental Makeup". Dementia Praecox Studies. 3 (1–2): 199–204.
- Matrikeledition der Universität Zürich Archived March 19, 2008, at the Wayback Machine.
- Frederick Tilney, Smith Ely Jelliffe: Semi-centennial Anniversary Volume of the American Neurological Association. American Neurological Association (1924)
- "Obituary". Journal of Nervous and Mental Disease, 70: 661–662 (1929)