Abstract: Altmetrics are web-based quantitative impact or attention indicators for academic articles that have been proposed to supplement citation counts. This article reports the first assessment of the extent to which mature altmetrics from this http URL and Mendeley associate with journal article quality. It exploits expert norm-referenced peer review scores from the UK Research Excellence Framework 2021 for 67,030+ journal articles in all fields 2014-17/18, split into 34 Units of Assessment (UoAs). The results show that altmetrics are better indicators of research quality than previously thought, although not as good as raw and field normalised Scopus citation counts. Surprisingly, field normalising citation counts can reduce their strength as a quality indicator for articles in a single field. For most UoAs, Mendeley reader counts are the best, tweet counts are also a relatively strong indicator in many fields, and Facebook, blogs and news citations are moderately strong indicators in some UoAs, at least in the UK. In general, altmetrics are the strongest indicators of research quality in the health and physical sciences and weakest in the arts and humanities. The Altmetric Attention Score, although hybrid, is almost as good as Mendeley reader counts as a quality indicator and reflects more non-scholarly impacts.