diff --git a/mesonbuild/backend/ninjabackend.py b/mesonbuild/backend/ninjabackend.py
index 8577bc77a..92d7dfb81 100644
--- a/mesonbuild/backend/ninjabackend.py
+++ b/mesonbuild/backend/ninjabackend.py
@@ -628,19 +628,24 @@ int dummy;
         self.generate_coverage_legacy_rules(outfile)
 
     def generate_coverage_legacy_rules(self, outfile):
-        (gcovr_exe, lcov_exe, genhtml_exe) = environment.find_coverage_tools()
+        (gcovr_exe, gcovr_3_1, lcov_exe, genhtml_exe) = environment.find_coverage_tools()
         added_rule = False
         if gcovr_exe:
+            # gcovr >= 3.1 interprets rootdir differently
+            if gcovr_3_1:
+                rootdir = self.environment.get_build_dir()
+            else:
+                rootdir = self.environment.get_source_dir(),
             added_rule = True
             elem = NinjaBuildElement(self.all_outputs, 'meson-coverage-xml', 'CUSTOM_COMMAND', '')
-            elem.add_item('COMMAND', [gcovr_exe, '-x', '-r', self.environment.get_source_dir(),
+            elem.add_item('COMMAND', [gcovr_exe, '-x', '-r', rootdir,
                                       '-o', os.path.join(self.environment.get_log_dir(), 'coverage.xml')])
             elem.add_item('DESC', 'Generating XML coverage report.')
             elem.write(outfile)
             # Alias that runs the target defined above
             self.create_target_alias('meson-coverage-xml', outfile)
             elem = NinjaBuildElement(self.all_outputs, 'meson-coverage-text', 'CUSTOM_COMMAND', '')
-            elem.add_item('COMMAND', [gcovr_exe, '-r', self.environment.get_source_dir(),
+            elem.add_item('COMMAND', [gcovr_exe, '-r', rootdir,
                                       '-o', os.path.join(self.environment.get_log_dir(), 'coverage.txt')])
             elem.add_item('DESC', 'Generating text coverage report.')
             elem.write(outfile)
diff --git a/mesonbuild/environment.py b/mesonbuild/environment.py
index ccd85d53e..099a3b3a9 100644
--- a/mesonbuild/environment.py
+++ b/mesonbuild/environment.py
@@ -77,19 +77,31 @@ cflags_mapping = {'c': 'CFLAGS',
                   'd': 'DFLAGS',
                   'vala': 'VALAFLAGS'}
 
+def detect_gcovr(version='3.1', log=False):
+    gcovr_exe = 'gcovr'
+    try:
+        p, found = Popen_safe([gcovr_exe, '--version'])[0:2]
+    except (FileNotFoundError, PermissionError):
+        # Doesn't exist in PATH or isn't executable
+        return
+    found = search_version(found)
+    if p.returncode == 0:
+        if log:
+            mlog.log('Found gcovr-{} at {}'.format(found, shlex.quote(shutil.which(gcovr_exe))))
+        return gcovr_exe, mesonlib.version_compare(found, '>=' + version)
 
 def find_coverage_tools():
-    gcovr_exe = 'gcovr'
+    gcovr_exe, gcovr_3_1 = detect_gcovr()
+
     lcov_exe = 'lcov'
     genhtml_exe = 'genhtml'
 
-    if not mesonlib.exe_exists([gcovr_exe, '--version']):
-        gcovr_exe = None
     if not mesonlib.exe_exists([lcov_exe, '--version']):
         lcov_exe = None
     if not mesonlib.exe_exists([genhtml_exe, '--version']):
         genhtml_exe = None
-    return gcovr_exe, lcov_exe, genhtml_exe
+
+    return gcovr_exe, gcovr_3_1, lcov_exe, genhtml_exe
 
 def detect_ninja(version='1.5', log=False):
     for n in ['ninja', 'ninja-build']:
diff --git a/mesonbuild/scripts/coverage.py b/mesonbuild/scripts/coverage.py
index 47f4cda29..4746134e0 100644
--- a/mesonbuild/scripts/coverage.py
+++ b/mesonbuild/scripts/coverage.py
@@ -17,15 +17,20 @@ from mesonbuild import environment
 import sys, os, subprocess, pathlib
 
 def coverage(source_root, build_root, log_dir):
-    (gcovr_exe, lcov_exe, genhtml_exe) = environment.find_coverage_tools()
+    (gcovr_exe, gcovr_3_1, lcov_exe, genhtml_exe) = environment.find_coverage_tools()
     if gcovr_exe:
+        # gcovr >= 3.1 interprets rootdir differently
+        if gcovr_3_1:
+            rootdir = build_root
+        else:
+            rootdir = source_root
         subprocess.check_call([gcovr_exe,
                                '-x',
-                               '-r', source_root,
+                               '-r', rootdir,
                                '-o', os.path.join(log_dir, 'coverage.xml'),
                                ])
         subprocess.check_call([gcovr_exe,
-                               '-r', source_root,
+                               '-r', rootdir,
                                '-o', os.path.join(log_dir, 'coverage.txt'),
                                ])
     if lcov_exe and genhtml_exe: