Witchers are often viewed with fear and suspicion by the common folk. Their unnatural abilities illicit apprehension, though none can deny their effectiveness in curtailing the vicious monsters that inhabit the lands, and most Witchers make their living hunting said beasts, monsters, and undead. According to the Netflix website, less than 50% of the children being trained as Witchers survive the ordeal known as the "Trial of Grasses." Geralt is already stronger than most, but he is also exposed to far more magic and alchemy than your standard issue Witcher, which results in him becoming even stronger.
The world of the "Witcher" already boasts several long-lived beings such as elves and mages. Elves possess natural longevity, while mages utilize magic to prolong their lifespans. Witchers fall into a separate category, and their transformation bestows them with incredibly long lives. However, no known upper limit exists for a Witcher due to their profession -– all of them are killed in the line of duty long before they ever get the chance to die of old age.
At the start of the Netflix series, Geralt is 71 years old, and at the beginning of Season 2, he will be 104. Vesemir (Kim Bodnia), Geralt's mentor who fans will meet in the new season, is 169, though he is reportedly quite a bit older in the books (via Netflix). Perhaps a definitive answer will be established when Season 2 comes out, or maybe the mystery will continue and fans will be left to simply speculate if Witchers are truly immortal.