diff --git a/src/Composer/Package/Version/VersionBumper.php b/src/Composer/Package/Version/VersionBumper.php
index bf9ed1fca..1129efaa0 100644
--- a/src/Composer/Package/Version/VersionBumper.php
+++ b/src/Composer/Package/Version/VersionBumper.php
@@ -71,7 +71,8 @@ class VersionBumper
         }
 
         $major = Preg::replace('{^(\d+).*}', '$1', $version);
-        $newPrettyConstraint = '^'.Preg::replace('{(?:\.(?:0|9999999))+(-dev)?$}', '', $version);
+        $versionWithoutSuffix = Preg::replace('{(?:\.(?:0|9999999))+(-dev)?$}', '', $version);
+        $newPrettyConstraint = '^'.$versionWithoutSuffix;
 
         // not a simple stable version, abort
         if (!Preg::isMatch('{^\^\d+(\.\d+)*$}', $newPrettyConstraint)) {
@@ -84,17 +85,24 @@ class VersionBumper
                 \^'.$major.'(?:\.\d+)* # e.g. ^2.anything
                 | ~'.$major.'(?:\.\d+)? # e.g. ~2 or ~2.2 but no more
                 | '.$major.'(?:\.[*x])+ # e.g. 2.* or 2.*.* or 2.x.x.x etc
+                | >=\d(?:\.\d+)* # e.g. >=2 or >=1.2 etc
             )
             (?=,|$|\ |\||@) # trailing separator
         }x';
         if (Preg::isMatchAllWithOffsets($pattern, $prettyConstraint, $matches)) {
             $modified = $prettyConstraint;
             foreach (array_reverse($matches['constraint']) as $match) {
+                assert(is_string($match[0]));
                 $suffix = '';
-                if (substr_count($match[0], '.') === 2 && substr_count($newPrettyConstraint, '.') === 1) {
+                if (substr_count($match[0], '.') === 2 && substr_count($versionWithoutSuffix, '.') === 1) {
                     $suffix = '.0';
                 }
-                $modified = substr_replace($modified, $newPrettyConstraint.$suffix, $match[1], Platform::strlen((string) $match[0]));
+                if (str_starts_with($match[0], '>=')) {
+                    $replacement = '>='.$versionWithoutSuffix.$suffix;
+                } else {
+                    $replacement = $newPrettyConstraint.$suffix;
+                }
+                $modified = substr_replace($modified, $replacement, $match[1], Platform::strlen($match[0]));
             }
 
             // if it is strictly equal to the previous one then no need to change anything
diff --git a/tests/Composer/Test/Package/Version/VersionBumperTest.php b/tests/Composer/Test/Package/Version/VersionBumperTest.php
index 3c55a42ff..1a53a898d 100644
--- a/tests/Composer/Test/Package/Version/VersionBumperTest.php
+++ b/tests/Composer/Test/Package/Version/VersionBumperTest.php
@@ -64,5 +64,7 @@ class VersionBumperTest extends TestCase
         yield 'leave patch wildcard alone' => ['2.4.3.*', '2.4.3.2', '2.4.3.*'];
         yield 'upgrade tilde to caret when compatible' => ['~2.2', '2.4.3', '^2.4.3'];
         yield 'leave patch-only-tilde alone' => ['~2.2.3', '2.2.6', '~2.2.3'];
+        yield 'upgrade bigger-or-eq to latest' => ['>=3.0', '3.4.5', '>=3.4.5'];
+        yield 'leave bigger-than untouched' => ['>2.2.3', '2.2.6', '>2.2.3'];
     }
 }