diff --git a/doc/source/whatsnew/v1.5.0.rst b/doc/source/whatsnew/v1.5.0.rst
index 8acf0ab3b7761..902279f44299e 100644
--- a/doc/source/whatsnew/v1.5.0.rst
+++ b/doc/source/whatsnew/v1.5.0.rst
@@ -566,6 +566,8 @@ I/O
 - Bug in Parquet roundtrip for Interval dtype with ``datetime64[ns]`` subtype (:issue:`45881`)
 - Bug in :func:`read_excel` when reading a ``.ods`` file with newlines between xml elements (:issue:`45598`)
 - Bug in :func:`read_parquet` when ``engine="fastparquet"`` where the file was not closed on error (:issue:`46555`)
+- :meth:`to_html` now excludes the ``border`` attribute from ``<table>`` elements when ``border`` keyword is set to ``False``.
+-
 
 Period
 ^^^^^^
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 1a28d9f44ae28..bcbd6437d6333 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -2892,7 +2892,7 @@ def to_html(
         classes: str | list | tuple | None = None,
         escape: bool = True,
         notebook: bool = False,
-        border: int | None = None,
+        border: int | bool | None = None,
         table_id: str | None = None,
         render_links: bool = False,
         encoding: str | None = None,
diff --git a/pandas/io/formats/format.py b/pandas/io/formats/format.py
index ea938c924ae0c..fd79d418658ea 100644
--- a/pandas/io/formats/format.py
+++ b/pandas/io/formats/format.py
@@ -1058,7 +1058,7 @@ def to_html(
         encoding: str | None = None,
         classes: str | list | tuple | None = None,
         notebook: bool = False,
-        border: int | None = None,
+        border: int | bool | None = None,
         table_id: str | None = None,
         render_links: bool = False,
     ) -> str | None:
diff --git a/pandas/io/formats/html.py b/pandas/io/formats/html.py
index 0c927277e899a..dfd95b96c68e8 100644
--- a/pandas/io/formats/html.py
+++ b/pandas/io/formats/html.py
@@ -44,7 +44,7 @@ def __init__(
         self,
         formatter: DataFrameFormatter,
         classes: str | list[str] | tuple[str, ...] | None = None,
-        border: int | None = None,
+        border: int | bool | None = None,
         table_id: str | None = None,
         render_links: bool = False,
     ) -> None:
@@ -57,8 +57,11 @@ def __init__(
         self.bold_rows = self.fmt.bold_rows
         self.escape = self.fmt.escape
         self.show_dimensions = self.fmt.show_dimensions
-        if border is None:
+        if border is None or border is True:
             border = cast(int, get_option("display.html.border"))
+        elif not border:
+            border = None
+
         self.border = border
         self.table_id = table_id
         self.render_links = render_links
@@ -237,8 +240,13 @@ def _write_table(self, indent: int = 0) -> None:
         else:
             id_section = f' id="{self.table_id}"'
 
+        if self.border is None:
+            border_attr = ""
+        else:
+            border_attr = f' border="{self.border}"'
+
         self.write(
-            f'<table border="{self.border}" class="{" ".join(_classes)}"{id_section}>',
+            f'<table{border_attr} class="{" ".join(_classes)}"{id_section}>',
             indent,
         )
 
diff --git a/pandas/tests/io/formats/test_to_html.py b/pandas/tests/io/formats/test_to_html.py
index aa8508d8e8942..3059efef09095 100644
--- a/pandas/tests/io/formats/test_to_html.py
+++ b/pandas/tests/io/formats/test_to_html.py
@@ -342,9 +342,9 @@ def test_to_html_truncate_multi_index(sparsify, expected, datapath):
     "option,result,expected",
     [
         (None, lambda df: df.to_html(), "1"),
-        (None, lambda df: df.to_html(border=0), "0"),
-        (0, lambda df: df.to_html(), "0"),
-        (0, lambda df: df._repr_html_(), "0"),
+        (None, lambda df: df.to_html(border=2), "2"),
+        (2, lambda df: df.to_html(), "2"),
+        (2, lambda df: df._repr_html_(), "2"),
     ],
 )
 def test_to_html_border(option, result, expected):
diff --git a/pandas/tests/io/test_html.py b/pandas/tests/io/test_html.py
index 99fa31726445a..ea50464155ad5 100644
--- a/pandas/tests/io/test_html.py
+++ b/pandas/tests/io/test_html.py
@@ -1148,6 +1148,25 @@ def test_to_html_timestamp(self):
         result = df.to_html()
         assert "2000-01-01" in result
 
+    def test_to_html_borderless(self):
+        df = DataFrame([{"A": 1, "B": 2}])
+        out_border_default = df.to_html()
+        out_border_true = df.to_html(border=True)
+        out_border_explicit_default = df.to_html(border=1)
+        out_border_nondefault = df.to_html(border=2)
+        out_border_zero = df.to_html(border=0)
+
+        out_border_false = df.to_html(border=False)
+
+        assert ' border="1"' in out_border_default
+        assert out_border_true == out_border_default
+        assert out_border_default == out_border_explicit_default
+        assert out_border_default != out_border_nondefault
+        assert ' border="2"' in out_border_nondefault
+        assert ' border="0"' not in out_border_zero
+        assert " border" not in out_border_false
+        assert out_border_zero == out_border_false
+
     @pytest.mark.parametrize(
         "displayed_only,exp0,exp1",
         [