diff --git a/python-package/lightgbm/dask.py b/python-package/lightgbm/dask.py
index b985c08757c7..27fedacb301e 100644
--- a/python-package/lightgbm/dask.py
+++ b/python-package/lightgbm/dask.py
@@ -11,7 +11,7 @@
 from copy import deepcopy
 from enum import Enum, auto
 from functools import partial
-from typing import Any, Callable, Dict, Iterable, List, Optional, Tuple, Type, Union
+from typing import Any, Dict, Iterable, List, Optional, Tuple, Type, Union
 from urllib.parse import urlparse
 
 import numpy as np
@@ -21,8 +21,8 @@
 from .compat import (DASK_INSTALLED, PANDAS_INSTALLED, SKLEARN_INSTALLED, Client, LGBMNotFittedError, concat,
                      dask_Array, dask_array_from_delayed, dask_bag_from_delayed, dask_DataFrame, dask_Series,
                      default_client, delayed, pd_DataFrame, pd_Series, wait)
-from .sklearn import (LGBMClassifier, LGBMModel, LGBMRanker, LGBMRegressor, _lgbmmodel_doc_custom_eval_note,
-                      _lgbmmodel_doc_fit, _lgbmmodel_doc_predict)
+from .sklearn import (LGBMClassifier, LGBMModel, LGBMRanker, LGBMRegressor, _LGBM_ScikitCustomEvalFunction,
+                      _lgbmmodel_doc_custom_eval_note, _lgbmmodel_doc_fit, _lgbmmodel_doc_predict)
 
 _DaskCollection = Union[dask_Array, dask_DataFrame, dask_Series]
 _DaskMatrixLike = Union[dask_Array, dask_DataFrame]
@@ -400,7 +400,7 @@ def _train(
     eval_class_weight: Optional[List[Union[dict, str]]] = None,
     eval_init_score: Optional[List[_DaskCollection]] = None,
     eval_group: Optional[List[_DaskVectorLike]] = None,
-    eval_metric: Optional[Union[Callable, str, List[Union[Callable, str]]]] = None,
+    eval_metric: Optional[Union[_LGBM_ScikitCustomEvalFunction, str, List[Union[_LGBM_ScikitCustomEvalFunction, str]]]] = None,
     eval_at: Optional[Iterable[int]] = None,
     **kwargs: Any
 ) -> LGBMModel:
@@ -1029,7 +1029,7 @@ def _lgb_dask_fit(
         eval_class_weight: Optional[List[Union[dict, str]]] = None,
         eval_init_score: Optional[List[_DaskCollection]] = None,
         eval_group: Optional[List[_DaskVectorLike]] = None,
-        eval_metric: Optional[Union[Callable, str, List[Union[Callable, str]]]] = None,
+        eval_metric: Optional[Union[_LGBM_ScikitCustomEvalFunction, str, List[Union[_LGBM_ScikitCustomEvalFunction, str]]]] = None,
         eval_at: Optional[Iterable[int]] = None,
         early_stopping_rounds: Optional[int] = None,
         **kwargs: Any
@@ -1096,7 +1096,7 @@ def __init__(
         learning_rate: float = 0.1,
         n_estimators: int = 100,
         subsample_for_bin: int = 200000,
-        objective: Optional[Union[Callable, str]] = None,
+        objective: Optional[str] = None,
         class_weight: Optional[Union[dict, str]] = None,
         min_split_gain: float = 0.,
         min_child_weight: float = 1e-3,
@@ -1165,7 +1165,7 @@ def fit(
         eval_sample_weight: Optional[List[_DaskVectorLike]] = None,
         eval_class_weight: Optional[List[Union[dict, str]]] = None,
         eval_init_score: Optional[List[_DaskCollection]] = None,
-        eval_metric: Optional[Union[Callable, str, List[Union[Callable, str]]]] = None,
+        eval_metric: Optional[Union[_LGBM_ScikitCustomEvalFunction, str, List[Union[_LGBM_ScikitCustomEvalFunction, str]]]] = None,
         early_stopping_rounds: Optional[int] = None,
         **kwargs: Any
     ) -> "DaskLGBMClassifier":
@@ -1281,7 +1281,7 @@ def __init__(
         learning_rate: float = 0.1,
         n_estimators: int = 100,
         subsample_for_bin: int = 200000,
-        objective: Optional[Union[Callable, str]] = None,
+        objective: Optional[str] = None,
         class_weight: Optional[Union[dict, str]] = None,
         min_split_gain: float = 0.,
         min_child_weight: float = 1e-3,
@@ -1348,7 +1348,7 @@ def fit(
         eval_names: Optional[List[str]] = None,
         eval_sample_weight: Optional[List[_DaskVectorLike]] = None,
         eval_init_score: Optional[List[_DaskVectorLike]] = None,
-        eval_metric: Optional[Union[Callable, str, List[Union[Callable, str]]]] = None,
+        eval_metric: Optional[Union[_LGBM_ScikitCustomEvalFunction, str, List[Union[_LGBM_ScikitCustomEvalFunction, str]]]] = None,
         early_stopping_rounds: Optional[int] = None,
         **kwargs: Any
     ) -> "DaskLGBMRegressor":
@@ -1446,7 +1446,7 @@ def __init__(
         learning_rate: float = 0.1,
         n_estimators: int = 100,
         subsample_for_bin: int = 200000,
-        objective: Optional[Union[Callable, str]] = None,
+        objective: Optional[str] = None,
         class_weight: Optional[Union[dict, str]] = None,
         min_split_gain: float = 0.,
         min_child_weight: float = 1e-3,
@@ -1516,7 +1516,7 @@ def fit(
         eval_sample_weight: Optional[List[_DaskVectorLike]] = None,
         eval_init_score: Optional[List[_DaskVectorLike]] = None,
         eval_group: Optional[List[_DaskVectorLike]] = None,
-        eval_metric: Optional[Union[Callable, str, List[Union[Callable, str]]]] = None,
+        eval_metric: Optional[Union[_LGBM_ScikitCustomEvalFunction, str, List[Union[_LGBM_ScikitCustomEvalFunction, str]]]] = None,
         eval_at: Iterable[int] = (1, 2, 3, 4, 5),
         early_stopping_rounds: Optional[int] = None,
         **kwargs: Any
diff --git a/python-package/lightgbm/sklearn.py b/python-package/lightgbm/sklearn.py
index 0ffbf17ea013..d83d98c97607 100644
--- a/python-package/lightgbm/sklearn.py
+++ b/python-package/lightgbm/sklearn.py
@@ -2,7 +2,7 @@
 """Scikit-learn wrapper interface for LightGBM."""
 import copy
 from inspect import signature
-from typing import Callable, Dict, Optional, Union
+from typing import Callable, Dict, List, Optional, Tuple, Union
 
 import numpy as np
 
@@ -11,14 +11,42 @@
 from .compat import (SKLEARN_INSTALLED, LGBMNotFittedError, _LGBMAssertAllFinite, _LGBMCheckArray,
                      _LGBMCheckClassificationTargets, _LGBMCheckSampleWeight, _LGBMCheckXY, _LGBMClassifierBase,
                      _LGBMComputeSampleWeight, _LGBMLabelEncoder, _LGBMModelBase, _LGBMRegressorBase, dt_DataTable,
-                     pd_DataFrame)
+                     pd_DataFrame, pd_Series)
 from .engine import train
 
+_ArrayLike = Union[List, np.ndarray, pd_Series]
+_EvalResultType = Tuple[str, float, bool]
+
+_LGBM_ScikitCustomObjectiveFunction = Union[
+    Callable[
+        [np.ndarray, np.ndarray],
+        Tuple[_ArrayLike, _ArrayLike]
+    ],
+    Callable[
+        [np.ndarray, np.ndarray, np.ndarray],
+        Tuple[_ArrayLike, _ArrayLike]
+    ],
+]
+_LGBM_ScikitCustomEvalFunction = Union[
+    Callable[
+        [np.ndarray, np.ndarray],
+        Union[_EvalResultType, List[_EvalResultType]]
+    ],
+    Callable[
+        [np.ndarray, np.ndarray, np.ndarray],
+        Union[_EvalResultType, List[_EvalResultType]]
+    ],
+    Callable[
+        [np.ndarray, np.ndarray, np.ndarray, np.ndarray],
+        Union[_EvalResultType, List[_EvalResultType]]
+    ],
+]
+
 
 class _ObjectiveFunctionWrapper:
     """Proxy class for objective function."""
 
-    def __init__(self, func):
+    def __init__(self, func: _LGBM_ScikitCustomObjectiveFunction):
         """Construct a proxy class.
 
         This class transforms objective function to match objective function with signature ``new_func(preds, dataset)``
@@ -107,7 +135,7 @@ def __call__(self, preds, dataset):
 class _EvalFunctionWrapper:
     """Proxy class for evaluation function."""
 
-    def __init__(self, func):
+    def __init__(self, func: _LGBM_ScikitCustomEvalFunction):
         """Construct a proxy class.
 
         This class transforms evaluation function to match evaluation function with signature ``new_func(preds, dataset)``
@@ -358,7 +386,7 @@ def __init__(
         learning_rate: float = 0.1,
         n_estimators: int = 100,
         subsample_for_bin: int = 200000,
-        objective: Optional[Union[str, Callable]] = None,
+        objective: Optional[Union[str, _LGBM_ScikitCustomObjectiveFunction]] = None,
         class_weight: Optional[Union[Dict, str]] = None,
         min_split_gain: float = 0.,
         min_child_weight: float = 1e-3,