diff --git a/Lib/fontTools/varLib/__init__.py b/Lib/fontTools/varLib/__init__.py
index 884c8550c..3efb2548c 100644
--- a/Lib/fontTools/varLib/__init__.py
+++ b/Lib/fontTools/varLib/__init__.py
@@ -811,14 +811,36 @@ def build(designspace, master_finder=lambda s:s, exclude=[], optimize=True):
 	return vf, model, master_ttfs
 
 
+def _open_font(path, master_finder):
+	# load TTFont masters from given 'path': this can be either a .TTX or an
+	# OpenType binary font; or if neither of these, try use the 'master_finder'
+	# callable to resolve the path to a valid .TTX or OpenType font binary.
+	from fontTools.ttx import guessFileType
+
+	master_path = os.path.normpath(path)
+	tp = guessFileType(master_path)
+	if tp is None:
+		# not an OpenType binary/ttx, fall back to the master finder.
+		master_path = master_finder(master_path)
+		tp = guessFileType(master_path)
+	if tp in ("TTX", "OTX"):
+		font = TTFont()
+		font.importXML(master_path)
+	elif tp in ("TTF", "OTF", "WOFF", "WOFF2"):
+		font = TTFont(master_path)
+	else:
+		raise VarLibError("Invalid master path: %r" % master_path)
+	return font
+
+
 def load_masters(designspace, master_finder=lambda s: s):
 	"""Ensure that all SourceDescriptor.font attributes have an appropriate TTFont
 	object loaded, or else open TTFont objects from the SourceDescriptor.path
 	attributes.
 
-	The paths can point to either an OpenType font or to a UFO. In the latter case,
-	use the provided master_finder callable to map from UFO paths to the respective
-	master font binaries (e.g. .ttf or .otf).
+	The paths can point to either an OpenType font, a TTX file, or a UFO. In the
+	latter case, use the provided master_finder callable to map from UFO paths to
+	the respective master font binaries (e.g. .ttf, .otf or .ttx).
 
 	Return list of master TTFont objects in the same order they are listed in the
 	DesignSpaceDocument.
@@ -845,15 +867,10 @@ def load_masters(designspace, master_finder=lambda s: s):
 						"Designspace source '%s' has neither 'font' nor 'path' "
 						"attributes" % (master.name or "<Unknown>")
 					)
-				# 2. A SourceDescriptor's path might point to a UFO or an OpenType
-				# binary. Find out the hard way.
-				master_path = os.path.normpath(master.path)
-				try:
-					font = TTFont(master_path)
-				except (IOError, TTLibError):
-					# 3. Not an OpenType binary, fall back to the master finder.
-					master_path = master_finder(master_path)
-					font = TTFont(master_path)
+				# 2. A SourceDescriptor's path might point an OpenType binary, a
+				# TTX file, or another source file (e.g. UFO), in which case we
+				# resolve the path using 'master_finder' function
+				font = _open_font(master.path, master_finder)
 				master_fonts.append(font)
 
 	return master_fonts
diff --git a/Tests/varLib/varLib_test.py b/Tests/varLib/varLib_test.py
index 6638ea363..16747fd7a 100644
--- a/Tests/varLib/varLib_test.py
+++ b/Tests/varLib/varLib_test.py
@@ -290,7 +290,7 @@ class BuildTest(unittest.TestCase):
         expected_ttx_path = self.get_test_output('BuildMain.ttx')
         self.expect_ttx(varfont, expected_ttx_path, tables)
 
-    def test_varlib_build_from_ds_object(self):
+    def test_varlib_build_from_ds_object_in_memory_ttfonts(self):
         ds_path = self.get_test_input("Build.designspace")
         ttx_dir = self.get_test_input("master_ttx_interpolatable_ttf")
         expected_ttx_path = self.get_test_output("BuildMain.ttx")
@@ -314,6 +314,44 @@ class BuildTest(unittest.TestCase):
         tables = [table_tag for table_tag in varfont.keys() if table_tag != "head"]
         self.expect_ttx(varfont, expected_ttx_path, tables)
 
+    def test_varlib_build_from_ttf_paths(self):
+        ds_path = self.get_test_input("Build.designspace")
+        ttx_dir = self.get_test_input("master_ttx_interpolatable_ttf")
+        expected_ttx_path = self.get_test_output("BuildMain.ttx")
+
+        self.temp_dir()
+        for path in self.get_file_list(ttx_dir, '.ttx', 'TestFamily-'):
+            self.compile_font(path, ".ttf", self.tempdir)
+
+        ds = DesignSpaceDocument.fromfile(ds_path)
+        for source in ds.sources:
+            source.path = os.path.join(
+                self.tempdir, os.path.basename(source.filename).replace(".ufo", ".ttf")
+            )
+        ds.updatePaths()
+
+        varfont, _, _ = build(ds)
+        varfont = reload_font(varfont)
+        tables = [table_tag for table_tag in varfont.keys() if table_tag != "head"]
+        self.expect_ttx(varfont, expected_ttx_path, tables)
+
+    def test_varlib_build_from_ttx_paths(self):
+        ds_path = self.get_test_input("Build.designspace")
+        ttx_dir = self.get_test_input("master_ttx_interpolatable_ttf")
+        expected_ttx_path = self.get_test_output("BuildMain.ttx")
+
+        ds = DesignSpaceDocument.fromfile(ds_path)
+        for source in ds.sources:
+            source.path = os.path.join(
+                ttx_dir, os.path.basename(source.filename).replace(".ufo", ".ttx")
+            )
+        ds.updatePaths()
+
+        varfont, _, _ = build(ds)
+        varfont = reload_font(varfont)
+        tables = [table_tag for table_tag in varfont.keys() if table_tag != "head"]
+        self.expect_ttx(varfont, expected_ttx_path, tables)
+
 
 def test_load_masters_layerName_without_required_font():
     ds = DesignSpaceDocument()