"We have failed to properly manage health risks at our semiconductor and LCD factories." Campaign groups say that 320 people have suffered from work-related illnesses after being employed by Samsung, with 118 of them dying.
Under a deal announced earlier this month, the firm will pay compensation of up to 150 million won (USD 133,000) per case.
It covers 16 types of cancer, some other rare illnesses, miscarriages and congenital diseases suffered by the workers' children.
The scandal emerged in 2007 when former workers at its semiconductor and display factories in Suwon, south of Seoul, and their families said that staff had been diagnosed or died of various forms of cancer.
A series of rulings and decisions by courts, Seoul's state labour welfare agency and a mediation committee followed over more than 10 years, culminating in Friday's announcement.
Relatives' leader Hwang Sang-gi, whose 22-year-old son died of leukaemia, said Friday: "The apology honestly was not enough for the families of the victims but we will accept it."