This is indeed one of FAQs on the Vikings. Please also check the following answers either by /u/sagathain, /u/Platypuskeeper, and myself in the following threads:
In short, the news reached also to Scandinavia, and out of Scandinavia in course of the 11th century. The oldest extant written account of Vinland was recorded in the late 11th century Germany.
Nevertheless, these points should be underlined here:
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As I explained before in: Why don’t we say Leif Erikson discovered the Americas, the modern (at least Scandinavian) historians since the early 20th century have been wary of accepting the historicity of Leif, as well as the event allegedly occurred more than 2 centuries before its recording in the parchments and only appeared in later saga traditions at face value.
In other words, Leif only appears in two medieval Icelandic sagas, put in writing more than 2 centuries after the original events (the exploration of Vinland) allegedly occurred. I don't say he was entirely invented by the later saga author(s) (there were probably some oral traditions on him also in the 13th and 14th century Iceland), but we are not sure whether he really played an important role in Vinland expedition as the later sagas claimed since the oldest written account of Vinland, transmitted and recorded in late 11th century Germany, does not allude to him at all.
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As for modern 're-discovery' of Leif and Vinland saga, the answers provided by /u/Platypuskeeper in: When did the Viking colonization of America become accepted by historians? might be a good starting point to explore.
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The term 'Markland' and its relevant latest news (alleged 'discovery' of hitherto little known pre-Columbian European source) appeared in this summer, I suppose we'll have to wait for more information right now. As for more details, please check the following two previous question threads in this subreddit:
(Edited): fixes typo.