diff --git a/conan/cli/command.py b/conan/cli/command.py
index 387112413e1..98cb9309c97 100644
--- a/conan/cli/command.py
+++ b/conan/cli/command.py
@@ -1,6 +1,6 @@
 import argparse
-import inspect
 import textwrap
+from contextlib import redirect_stdout
 
 from conan.api.output import ConanOutput
 from conan.errors import ConanException
@@ -68,6 +68,8 @@ def _init_formatters(self, parser):
         if formatters:
             help_message = "Select the output format: {}".format(", ".join(formatters))
             parser.add_argument('-f', '--format', action=OnceArgument, help=help_message)
+        parser.add_argument("--out-file", action=OnceArgument,
+                            help="Write the output of the command to the specified file instead of stdout.")
 
     @property
     def name(self):
@@ -84,7 +86,7 @@ def doc(self):
     def _format(self, parser, info, *args):
         parser_args, _ = parser.parse_known_args(*args)
 
-        formatarg = getattr(parser_args, "format", "text")
+        formatarg = getattr(parser_args, "format", None) or "text"
         out_file = getattr(parser_args, "out_file", None)
 
         try:
@@ -93,8 +95,11 @@ def _format(self, parser, info, *args):
             raise ConanException("{} is not a known format. Supported formatters are: {}".format(
                 formatarg, ", ".join(self._help_formatters)))
 
-        if out_file and "out_file" in inspect.signature(formatter).parameters.keys():
-            formatter(info, out_file=out_file)
+        if out_file:
+            with open(out_file, 'w') as f:
+                with redirect_stdout(f):
+                    formatter(info)
+            ConanOutput().info(f"Formatted output saved to '{out_file}'")
         else:
             formatter(info)
 
diff --git a/conan/cli/commands/graph.py b/conan/cli/commands/graph.py
index 3d4c3218713..2b55a4b6718 100644
--- a/conan/cli/commands/graph.py
+++ b/conan/cli/commands/graph.py
@@ -5,7 +5,7 @@
 from conan.api.output import ConanOutput, cli_out_write, Color
 from conan.cli import make_abs_path
 from conan.cli.args import common_graph_args, validate_common_graph_args
-from conan.cli.command import conan_command, conan_subcommand, OnceArgument
+from conan.cli.command import conan_command, conan_subcommand
 from conan.cli.commands.list import prepare_pkglist_compact, print_serial
 from conan.cli.formatters.graph import format_graph_html, format_graph_json, format_graph_dot
 from conan.cli.formatters.graph.build_order_html import format_build_order_html
@@ -192,8 +192,6 @@ def graph_info(conan_api, parser, subparser, *args):
                            help="Deployer output folder, base build folder by default if not set")
     subparser.add_argument("--build-require", action='store_true', default=False,
                            help='Whether the provided reference is a build-require')
-    subparser.add_argument("--out-file", action=OnceArgument,
-                           help="Filename of the file to save the output of the formatter.")
 
     args = parser.parse_args(*args)
 
diff --git a/conan/cli/formatters/graph/graph.py b/conan/cli/formatters/graph/graph.py
index 23034b65c62..6b174f603cd 100644
--- a/conan/cli/formatters/graph/graph.py
+++ b/conan/cli/formatters/graph/graph.py
@@ -11,7 +11,7 @@
     BINARY_DOWNLOAD, BINARY_BUILD, BINARY_MISSING, BINARY_UPDATE
 from conans.client.graph.graph_error import GraphConflictError
 from conans.client.installer import build_id
-from conans.util.files import load, save
+from conans.util.files import load
 
 
 # FIXME: Check all this code when format_graph_[html/dot] use serialized graph
@@ -138,15 +138,11 @@ def format_graph_dot(result):
     cli_out_write(_render_graph(graph, None, template, template_folder))
 
 
-def format_graph_json(result, out_file=None):
+def format_graph_json(result):
     graph = result["graph"]
     field_filter = result.get("field_filter")
     package_filter = result.get("package_filter")
     serial = graph.serialize()
     serial = filter_graph(serial, package_filter=package_filter, field_filter=field_filter)
     json_result = json.dumps({"graph": serial}, indent=4)
-    if out_file is not None:
-        ConanOutput().info(f"Formatted output saved to '{out_file}'")
-        save(out_file, json_result)
-        return
     cli_out_write(json_result)
diff --git a/test/integration/command/info/info_test.py b/test/integration/command/info/info_test.py
index eab7c4849be..8f254820a40 100644
--- a/test/integration/command/info/info_test.py
+++ b/test/integration/command/info/info_test.py
@@ -435,12 +435,3 @@ def requirements(self):
 
     c.run("graph info . -c tools.graph:vendor=build --build='lib*'")
     c.assert_listed_binary({"lib/1.0": (NO_SETTINGS_PACKAGE_ID, "Build")})
-
-
-def test_write_formatter_to_file():
-    c = TestClient(light=True)
-    c.save({"conanfile.py":  GenConanfile("pkg", "0.1")})
-    c.run("graph info .  --format=json --out-file=graph.json")
-    assert "Formatted output saved to 'graph.json'" in c.out
-    graph = json.loads(c.load("graph.json"))
-    assert len(graph["graph"]["nodes"]) == 1
diff --git a/test/integration/command_v2/test_output.py b/test/integration/command_v2/test_output.py
index 534f2c46525..053588b1432 100644
--- a/test/integration/command_v2/test_output.py
+++ b/test/integration/command_v2/test_output.py
@@ -1,3 +1,5 @@
+import json
+
 from conan.test.assets.genconanfile import GenConanfile
 from conan.test.utils.tools import TestClient
 from conan.test.utils.env import environment_update
@@ -260,3 +262,32 @@ def test_exception_errors(self):
         t.run("create . -vquiet", assert_error=True)
         assert "ERROR: Tagged error" not in t.out
         assert "ConanException: Untagged error" not in t.out
+
+
+def test_formatter_redirection_to_file():
+    c = TestClient(light=True)
+    c.save({"conanfile.py":  GenConanfile("pkg", "0.1")})
+
+    c.run("config home --out-file=cmd_out.txt")
+    assert "Formatted output saved to 'cmd_out.txt'" in c.out
+    cmd_out = c.load("cmd_out.txt")
+    assert f"{c.cache_folder}\n" == cmd_out
+    assert not f"{c.cache_folder}\n" == c.stdout
+
+    c.run("graph info .  --format=json --out-file=graph.json")
+    assert "Formatted output saved to 'graph.json'" in c.out
+    graph = json.loads(c.load("graph.json"))
+    assert len(graph["graph"]["nodes"]) == 1
+    assert not "nodes" in c.stdout
+
+    c.run("graph info .  --format=html --out-file=graph.html")
+    assert "Formatted output saved to 'graph.html'" in c.out
+    html = c.load("graph.html")
+    assert "<head>" in html
+    assert not "<head>" in c.stdout
+
+    c.run("install .  --format=json --out-file=graph.json")
+    assert "Formatted output saved to 'graph.json'" in c.out
+    graph = json.loads(c.load("graph.json"))
+    assert len(graph["graph"]["nodes"]) == 1
+    assert not "nodes" in c.stdout