diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 2782ee7b9d201..02d9cc5cbdf30 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -1678,9 +1678,10 @@ def to_parquet(self, fname, engine='auto', compression='snappy',
         fname : str
             string file path
         engine : {'auto', 'pyarrow', 'fastparquet'}, default 'auto'
-            Parquet reader library to use. If 'auto', then the option
-            'io.parquet.engine' is used. If 'auto', then the first
-            library to be installed is used.
+            Parquet library to use. If 'auto', then the option
+            ``io.parquet.engine`` is used. The default ``io.parquet.engine``
+            behavior is to try 'pyarrow', falling back to 'fastparquet' if
+            'pyarrow' is unavailable.
         compression : {'snappy', 'gzip', 'brotli', None}, default 'snappy'
             Name of the compression to use. Use ``None`` for no compression.
         kwargs
diff --git a/pandas/io/parquet.py b/pandas/io/parquet.py
index 1c22a305c089d..a99014f07a6b3 100644
--- a/pandas/io/parquet.py
+++ b/pandas/io/parquet.py
@@ -244,9 +244,10 @@ def to_parquet(df, path, engine='auto', compression='snappy', **kwargs):
     path : string
         File path
     engine : {'auto', 'pyarrow', 'fastparquet'}, default 'auto'
-        Parquet reader library to use. If 'auto', then the option
-        'io.parquet.engine' is used. If 'auto', then the first
-        library to be installed is used.
+        Parquet library to use. If 'auto', then the option
+        ``io.parquet.engine`` is used. The default ``io.parquet.engine``
+        behavior is to try 'pyarrow', falling back to 'fastparquet' if
+        'pyarrow' is unavailable.
     compression : {'snappy', 'gzip', 'brotli', None}, default 'snappy'
         Name of the compression to use. Use ``None`` for no compression.
     kwargs
@@ -271,9 +272,10 @@ def read_parquet(path, engine='auto', columns=None, **kwargs):
 
         .. versionadded 0.21.1
     engine : {'auto', 'pyarrow', 'fastparquet'}, default 'auto'
-        Parquet reader library to use. If 'auto', then the option
-        'io.parquet.engine' is used. If 'auto', then the first
-        library to be installed is used.
+        Parquet library to use. If 'auto', then the option
+        ``io.parquet.engine`` is used. The default ``io.parquet.engine``
+        behavior is to try 'pyarrow', falling back to 'fastparquet' if
+        'pyarrow' is unavailable.
     kwargs are passed to the engine
 
     Returns