BAME, which stands for black, Asian and minority ethnic, has been widely used as a catch-all in discussions relating to race and inclusion, but has faced criticism over its lack of nuance.
ITN said it will move away from using the acronym in "newsrooms and corporate communications".
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The broadcasters hope the move will inspire similar action across the creative industries.
The authors of the report from the LHC said: "We believe that, while there can still be utility in the use of collective terms, the priority should always be to ensure clear and simple communication that is trusted by audiences.
"We hope that our report will help broadcasters to achieve this, and, as language develops, they regularly revisit this and related issues."
The listed authors of the document - which draws on interviews with journalists, academics, audience focus groups and more - are Sarita Malik, Marcus Ryder, Stevie Marsden, Robert Lawson and Matt Gee.
BAME, which is not used widely outside the UK, has its roots in the anti-racist movement in the 1970s and, according to the report, has become "the preferred dominant term" to describe non-white groups, especially since 2020.
The report says the acronym should never be used verbally and generally recommends against its use in writing.
The term, however, can be used in reported speech but should always be written out in full to ensure against the "homogenising of all 'non-white' ethnic groups".
Miranda Wayland, BBC head of creative and workforce diversity and inclusion, said: "We're proud to have collaborated with our broadcasting partners and the Sir Lenny Henry Centre for Media Diversity on this important work.
"Ensuring that the rich and complex lived experiences of individual ethnic groups are accurately reflected and truthfully portrayed on air and properly recognised in our workplace speaks to our ongoing commitment and investment in greater inclusion."