diff --git a/var/spack/repos/builtin/packages/proj/package.py b/var/spack/repos/builtin/packages/proj/package.py
index a49adf19b8cb6..01107a698fbe2 100644
--- a/var/spack/repos/builtin/packages/proj/package.py
+++ b/var/spack/repos/builtin/packages/proj/package.py
@@ -85,6 +85,9 @@ class Proj(CMakePackage, AutotoolsPackage):
         when="@7:7.2.1",
     )
 
+    patch("proj.cmakelists.5.0.patch", when="@5.0")
+    patch("proj.cmakelists.5.1.patch", when="@5.1:5.2")
+
     # https://proj.org/install.html#build-requirements
     with when("build_system=cmake"):
         depends_on("cmake@3.9:", when="@6:", type="build")
@@ -137,6 +140,13 @@ def cmake_args(self):
         ]
         if self.spec.satisfies("@6:") and self.pkg.run_tests:
             args.append(self.define("USE_EXTERNAL_GTEST", True))
+        if self.spec.satisfies("@7:"):
+            test_flag = "BUILD_TESTING"
+        elif self.spec.satisfies("@5.1:"):
+            test_flag = "PROJ_TESTS"
+        else:
+            test_flag = "PROJ4_TESTS"
+        args.append(self.define(test_flag, self.pkg.run_tests))
         return args
 
 
diff --git a/var/spack/repos/builtin/packages/proj/proj.cmakelists.5.0.patch b/var/spack/repos/builtin/packages/proj/proj.cmakelists.5.0.patch
new file mode 100644
index 0000000000000..02302bce9dc69
--- /dev/null
+++ b/var/spack/repos/builtin/packages/proj/proj.cmakelists.5.0.patch
@@ -0,0 +1,12 @@
+diff --git a/CMakeLists.txt b/CMakeLists.txt
+--- a/CMakeLists.txt
++++ b/CMakeLists.txt
+@@ -149,5 +149,6 @@ add_subdirectory(nad)
+ add_subdirectory(src)
+ add_subdirectory(man)
+ add_subdirectory(cmake)
+-add_subdirectory(test)
+-
++if(PROJ4_TESTS)
++  add_subdirectory(test)
++endif(PROJ4_TESTS)
diff --git a/var/spack/repos/builtin/packages/proj/proj.cmakelists.5.1.patch b/var/spack/repos/builtin/packages/proj/proj.cmakelists.5.1.patch
new file mode 100644
index 0000000000000..fb4ad9b052b77
--- /dev/null
+++ b/var/spack/repos/builtin/packages/proj/proj.cmakelists.5.1.patch
@@ -0,0 +1,12 @@
+diff --git a/CMakeLists.txt b/CMakeLists.txt
+--- a/CMakeLists.txt
++++ b/CMakeLists.txt
+@@ -159,5 +159,6 @@ add_subdirectory(nad)
+ add_subdirectory(src)
+ add_subdirectory(man)
+ add_subdirectory(cmake)
+-add_subdirectory(test)
+-
++if(PROJ_TESTS)
++  add_subdirectory(test)
++endif(PROJ_TESTS)