diff --git a/completions/fish/brew.fish b/completions/fish/brew.fish
index 544da34d88..900c09d906 100644
--- a/completions/fish/brew.fish
+++ b/completions/fish/brew.fish
@@ -1922,7 +1922,7 @@ __fish_brew_complete_arg 'upgrade' -l fontdir -d 'Target location for Fonts (def
 __fish_brew_complete_arg 'upgrade' -l force -d 'Install formulae without checking for previously installed keg-only or non-migrated versions. When installing casks, overwrite existing files (binaries and symlinks are excluded, unless originally from the same cask)'
 __fish_brew_complete_arg 'upgrade' -l force-bottle -d 'Install from a bottle if it exists for the current or newest version of macOS, even if it would not normally be used for installation'
 __fish_brew_complete_arg 'upgrade' -l formula -d 'Treat all named arguments as formulae. If no named arguments are specified, upgrade only outdated formulae'
-__fish_brew_complete_arg 'upgrade' -l greedy -d 'Also include casks with `auto_updates true` or `version :latest`'
+__fish_brew_complete_arg 'upgrade' -l greedy -d 'Also include casks with `auto_updates true` or `version :latest`. Enabled by default if `$HOMEBREW_UPGRADE_GREEDY` is set'
 __fish_brew_complete_arg 'upgrade' -l greedy-auto-updates -d 'Also include casks with `auto_updates true`'
 __fish_brew_complete_arg 'upgrade' -l greedy-latest -d 'Also include casks with `version :latest`'
 __fish_brew_complete_arg 'upgrade' -l help -d 'Show this message'
diff --git a/completions/zsh/_brew b/completions/zsh/_brew
index 357def9c7e..bcab5eb99c 100644
--- a/completions/zsh/_brew
+++ b/completions/zsh/_brew
@@ -2365,7 +2365,7 @@ _brew_upgrade() {
     '(--formula)--fontdir[Target location for Fonts (default: `~/Library/Fonts`)]' \
     '--force[Install formulae without checking for previously installed keg-only or non-migrated versions. When installing casks, overwrite existing files (binaries and symlinks are excluded, unless originally from the same cask)]' \
     '(--cask --build-from-source)--force-bottle[Install from a bottle if it exists for the current or newest version of macOS, even if it would not normally be used for installation]' \
-    '(--formula)--greedy[Also include casks with `auto_updates true` or `version :latest`]' \
+    '(--formula)--greedy[Also include casks with `auto_updates true` or `version :latest`. Enabled by default if `$HOMEBREW_UPGRADE_GREEDY` is set]' \
     '(--formula)--greedy-auto-updates[Also include casks with `auto_updates true`]' \
     '(--formula)--greedy-latest[Also include casks with `version :latest`]' \
     '--help[Show this message]' \
diff --git a/docs/Manpage.md b/docs/Manpage.md
index 485221bd24..cfdafbb973 100644
--- a/docs/Manpage.md
+++ b/docs/Manpage.md
@@ -1754,7 +1754,8 @@ for the upgraded formulae or, every 30 days, for all formulae.
 
 `-g`, `--greedy`
 
-: Also include casks with `auto_updates true` or `version :latest`.
+: Also include casks with `auto_updates true` or `version :latest`. Enabled by
+  default if `$HOMEBREW_UPGRADE_GREEDY` is set.
 
 `--greedy-latest`
 
diff --git a/manpages/brew.1 b/manpages/brew.1
index 1678fe2dbe..5981153260 100644
--- a/manpages/brew.1
+++ b/manpages/brew.1
@@ -1084,7 +1084,7 @@ Treat all named arguments as casks\. If no named arguments are specified, upgrad
 Skip installing cask dependencies\.
 .TP
 \fB\-g\fP, \fB\-\-greedy\fP
-Also include casks with \fBauto_updates true\fP or \fBversion :latest\fP\&\.
+Also include casks with \fBauto_updates true\fP or \fBversion :latest\fP\&\. Enabled by default if \fB$HOMEBREW_UPGRADE_GREEDY\fP is set\.
 .TP
 \fB\-\-greedy\-latest\fP
 Also include casks with \fBversion :latest\fP\&\.