Around 1,300 people could be eligible for the immunotherapy drugs every year, and people with advanced skin cancer currently live less than two years on average.
Nice moved quickly on the drug approval after the results of a phase II study into the drugs showed startling results in April.
Of 95 patients given the combined treatment, more than 60% were still alive after two years and, of those, a fifth 22% had no detectable tumours remaining.
Each blocks a separate receptor switch on immune system T-cells that weakens the immune response and can be activated by molecules released by tumours.
Checkpoint inhibitors can have side effects, including causing diarrhoea and liver damage.
Research presented at the American Society of Clinical Oncology Asco conference last week showed that of 38 patients given the drugs, 47% responded, with more than 83% still alive after a year.