diff --git a/.changes/unreleased/Under the Hood-20240502-154430.yaml b/.changes/unreleased/Under the Hood-20240502-154430.yaml
new file mode 100644
index 00000000000..6c17df3a6c6
--- /dev/null
+++ b/.changes/unreleased/Under the Hood-20240502-154430.yaml	
@@ -0,0 +1,6 @@
+kind: Under the Hood
+body: Clear error message for Private package in dbt-core
+time: 2024-05-02T15:44:30.713097-07:00
+custom:
+  Author: ChenyuLInx
+  Issue: "10083"
diff --git a/core/dbt/contracts/project.py b/core/dbt/contracts/project.py
index 4b98143f4b4..b0b7179f333 100644
--- a/core/dbt/contracts/project.py
+++ b/core/dbt/contracts/project.py
@@ -78,6 +78,16 @@ def get_revisions(self) -> List[str]:
             return [str(self.revision)]
 
 
+@dataclass
+class PrivatePackage(Package):
+    private: str
+    provider: Optional[str] = None
+    revision: Optional[RawVersion] = None
+    warn_unpinned: Optional[bool] = field(default=None, metadata={"alias": "warn-unpinned"})
+    subdirectory: Optional[str] = None
+    unrendered: Dict[str, Any] = field(default_factory=dict)
+
+
 @dataclass
 class RegistryPackage(Package):
     package: str
@@ -92,7 +102,7 @@ def get_versions(self) -> List[str]:
             return [str(self.version)]
 
 
-PackageSpec = Union[LocalPackage, TarballPackage, GitPackage, RegistryPackage]
+PackageSpec = Union[LocalPackage, TarballPackage, GitPackage, RegistryPackage, PrivatePackage]
 
 
 @dataclass
diff --git a/core/dbt/deps/resolver.py b/core/dbt/deps/resolver.py
index 0ac27835511..b4a0c60ef6c 100644
--- a/core/dbt/deps/resolver.py
+++ b/core/dbt/deps/resolver.py
@@ -7,6 +7,7 @@
     GitPackage,
     LocalPackage,
     PackageSpec,
+    PrivatePackage,
     RegistryPackage,
     TarballPackage,
 )
@@ -16,7 +17,7 @@
 from dbt.deps.registry import RegistryUnpinnedPackage
 from dbt.deps.tarball import TarballUnpinnedPackage
 from dbt.exceptions import (
-    DbtInternalError,
+    DependencyError,
     DuplicateDependencyToRootError,
     DuplicateProjectDependencyError,
     MismatchedDependencyTypeError,
@@ -74,10 +75,14 @@ def update_from(self, src: List[PackageSpec]) -> None:
                 pkg = TarballUnpinnedPackage.from_contract(contract)
             elif isinstance(contract, GitPackage):
                 pkg = GitUnpinnedPackage.from_contract(contract)
+            elif isinstance(contract, PrivatePackage):
+                raise DependencyError(
+                    f'Cannot resolve private package {contract.private} because git provider integration is missing. Please use a "git" package instead.'
+                )
             elif isinstance(contract, RegistryPackage):
                 pkg = RegistryUnpinnedPackage.from_contract(contract)
             else:
-                raise DbtInternalError("Invalid package type {}".format(type(contract)))
+                raise DependencyError("Invalid package type {}".format(type(contract)))
             self.incorporate(pkg)
 
     @classmethod
diff --git a/tests/functional/configs/test_custom_node_colors_configs.py b/tests/functional/configs/test_custom_node_colors_configs.py
index 1ca28d67795..7772e3d44ca 100644
--- a/tests/functional/configs/test_custom_node_colors_configs.py
+++ b/tests/functional/configs/test_custom_node_colors_configs.py
@@ -1,5 +1,6 @@
 import pytest
 
+from dbt.exceptions import ConfigUpdateError
 from dbt.tests.util import get_manifest, run_dbt
 from dbt_common.dataclass_schema import ValidationError
 
@@ -304,7 +305,7 @@ def test__invalid_color_config_block(
         self,
         project,
     ):
-        with pytest.raises(ValidationError):
+        with pytest.raises((ValidationError, ConfigUpdateError)):
             run_dbt(["compile"])
 
 
diff --git a/tests/unit/test_deps.py b/tests/unit/test_deps.py
index 1ca640c50c3..339bbbc5d23 100644
--- a/tests/unit/test_deps.py
+++ b/tests/unit/test_deps.py
@@ -791,6 +791,19 @@ def test_dependency_resolution(self):
         self.assertEqual(resolved[1].name, "dbt-labs-test/b")
         self.assertEqual(resolved[1].version, "0.2.1")
 
+    def test_private_package_raise_error(self):
+        package_config = PackageConfig.from_dict(
+            {
+                "packages": [
+                    {"private": "dbt-labs-test/a", "subdirectory": "foo-bar"},
+                ],
+            }
+        )
+        with self.assertRaisesRegex(
+            dbt.exceptions.DependencyError, "Cannot resolve private package"
+        ):
+            resolve_packages(package_config.packages, mock.MagicMock(project_name="test"), {})
+
     def test_dependency_resolution_allow_prerelease(self):
         package_config = PackageConfig.from_dict(
             {