This depended on what area we're talking about. Scholars of modern China tended to be the quickest to adapt, those writing on pre-modern China tended to hold onto Wade-Giles, sometimes stubbornly. Others continued to use Wade-Giles for reasons of consistency. For example, the Cambridge History of China was begun at a time when Wade-Giles was standard in English language scholarship. New volumes continue to appear, but they've stuck with Wade-Giles to conform with the spelling conventions of earlier editions. So, in 2016, they published The Ch'ing Dynasty to 1800, Part 2. Note that "Ch'ing" is the Wade-Giles spelling of "Qing". The China Quarterly (a major journal of the field) preferred for similar reasons of consistency to put their "pinyin debut" off until the first issue of 1980.
These consistency problems cause many to continue to refer to the Nationalist Party (國民黨) as the Kuomintang (KMT) rather than the Guomindang (GMD). This is a phenomenon that doesn't only occur in the academy. Some brands are allowed by special permission of the Chinese government to continue to use Wade-Giles spellings in their brand names, for example Tsinghua University (which would be Qinghua in pinyin).
The point of no return was really the adoption of pinyin by the US Library of Congress in 2000, after rejecting it in the late 1970s. When this was announced in 1997 it was welcomed by librarians (although there were and remain grumblings about word division) mainly because by then everyone was using it. Really, the change came long before that. The British Library for example was already using pinyin in 1966. In 1979, the PRC officially announced that all foreign-language publications would use hanyu pinyin. That same year, the US Board on Geographic Names published an official conversion chart. By the 1990s, library scholars were recommending the "complete abandonment of Wade-Giles in favor of Hanyu Pinyin" (Tao and Cole).
Scholars of pre-modern China held on to Wade-Giles for a bit longer. Charles Hucker, in his 1985 Dictionary of Official Titles in Imperial China (which remains the standard to this day), wrote that Wade-Giles "is still preferred by so many Sinologists that for the foreseeable future no pre modern China specialist can afford not to know [it]". This remains true to this day — you need to know it for accessing older texts — but nowadays few would use Wade-Giles in their own publications. At most, a conversion table might be included as a convenience. For the scholar of pre-modern China, all you need to know is that Endymion Wilkinson's 1998 Chinese History: A Manual used pinyin. That's the gold standard right there.
Perhaps the last bastion of Wade-Giles is religious studies. Many prefer T'ao to Dao, for example (although it doesn't really matter when it comes to the word(s) "Taoism/T'aoism/Daoism", as none of them are Chinese anyway). Or T'ai Chi instead of Taiji, or I Ching instead of Yijing. Some academics who can't read Chinese still use Wade-Giles, but in my experience this is because they don't know the difference and sometimes use a mixture of Wade-Giles and pinyin spellings.
Finally, I should note that we're only talking about English language sources here. France and Germany have their own romanisation systems, which I confess I know little about, but Wade-Giles was never dominant there. This highlights the confusion some people have with pinyin: it's not supposed to be a replacement for Wade-Giles. It's not based on English at all. This leads to some wrong-headed criticisms of pinyin, which certainly isn't a perfect system, but neither was it designed to be a new Wade-Giles.
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edit: formatting