Definitely the Japanese. Considering they were "discovered" to have White status by the South Africans as late as the mid-20th century.

This answer is only half joking, because White as a "race" (and "race" itself) is an entirely socially constructed (and modern) phenomenon.

For reference, consider this litmus test. Obama is half-"white", half-"black". Do you consider him black or white? Norah Jones is half-"white", half-"indian". Is she white or indian? Certain groups are "allowed" to be half-white, amongst which Asians are high up on the list. Black, unfortunately according to our society, are never allowed to be (or never functionally recognized as) half-white.

Are Greeks white? What about Turks? What about the fact that genetically (and visually) they are quite similar?

So long story short, the last "white tribe" to be discovered will be the last group of people we've decided that we're going to include as "white."

To take a different take on what /u/bitparity said, the thing about uncontacted people more generally is that, very quickly, you realize that they were normally in contact with other people around them... just not in contact with Europeans. Even Andaman Islanders (the Sentinelese probably have one of the few claims on being uncontacted groups in the Eastern Hemisphere) seem to have been in contact with each other, at the very least (more on them here because they're fascinating). Aboriginal Australians seem to have been minimally in contact with Torres Straight Islanders, who seem to have been part of a larger trade system that goes all through the Indonesian archipelago to China, for instance.

So uncontacted seems to mean "not in contact with a European state or a European-style New World state, or sometimes a Middle Eastern, South Asian, or East Asian state, depending on what we mean." As bit points out, the idea of race is a very contingent one, depending a lot on the moment when we're speaking. If we take "white" to mean "in the continent of Europe", and "contact" means not just "occasional trade contact" but "incorporation into a state system", the answer could well certainly the Sami peoples of northern Fennoscandia...but these people are in Scandinavian records since written records appear in Northern Scandinavia. While there have been lots of debates by Victorian scientific racists about whether the Sami count as "White" or not, what limited genetic studies there are suggest that they (unsurprisingly) mostly share genetic descent with other Europeans.

If Whiteness extends beyond the Ural Mountains which form the traditional eastern bound of Europe, and we count other Finno-Ugric or even Samoyedic peoples (the two are sometimes classified linguistically together as "Uralic Languages") as "white", then those groups were the last groups would probably be the last groups to be incorporated into a European-style state system as Imperial Russia expanded eastward between the 17th and 19th centuries, and then the Soviets made efforts to further incoprorate these groups into the state by doing things like collectivizing reindeer cultivation. People like the Nenets, one of the Uralic groups most geographically distant from Europe, have appeared in European records since the 9th century, at least according to Wikipedia. Other Samoyedic groups, like the Nganasans may not have had direct regular contact with Russians until the 17th century, but they certainly had other trading relationships before then.

If you count other indigenous Siberians broadly as White, there may be groups that were not in direct, regular contact with a major state system (Russian, Mongolian, or Chinese) until the 19th century, but I'm not sure if you would count those as "White" because, as Bit points out, race is very good at saying "We are clearly different from that far away group of Africans, or East Asians, or South Asians, or aboriginal Americans and Australians, whatever" but is generally much worse at drawing a line clear dividing line among the dozens of small groups that traditionally dominated the space between, say, Moscow (White) and Beijing (Asian), or even as Bit points out the rather large groups between say Belgrade (White) and Karachi (Asian), or for that matter the groups between Karachi (Asian) and Beijing (Asian, but often seen as a different kind). That's what we mean when say it's socially constructed: it's not that there's no differences, it's that how we draw the categorical boundaries between groups that exist over a continuum is a more or less arbitrary decision that people then more or less agree on.