The male patient, 54, was "doing well under the circumstances" after the 15-hour operation on July 25-26, the clinic at the Technical University in the southern city of Munich said.
The amputee, who had lived without arms for six years since the accident, consulted the 40-member team at the university's Rechts der Isar Clinic after two failed attempts to use various artificial prostheses.
"The man required round-the-clock assistance - a condition he wanted to change as quickly as possible," the clinic said in a statement.
The facility had a decades-old unit for microsurgery and replantation surgery with a speciality in interdisciplinary operations it said was essential for a procedure of this complexity.
Professor Hans-Guenther Machens had prepared the transplant since he became the clinic's director in December.
It said suppressing the man's immune system so it would not reject the new limbs was a key concern.
Another key challenge was finding a donor who matched the patient's sex, age, skin colour, size and blood type.