Links in Excel have cell formatting (generally blue text and an underline) like any other formatted text.

If no other formatting is specified for links in XlsxWriter the module adds a default (blue underline) format, like Excel does when you enter a url. This is explained in the write_url() docs.

However, if the user specifies a format for a cell with a link (like the text_wrap format in your example) then it overrides the default format.

So if you want blue underline plus text wrap format for urls you will have to specify it directly:

import xlsxwriter

workbook = xlsxwriter.Workbook('my_export.xlsx')
worksheet = workbook.add_worksheet(name='export_object1')

link_format = workbook.add_format({'color': 'blue', 
                                   'underline': True, 
                                   'text_wrap': True})

text_format = workbook.add_format({'text_wrap': True})

worksheet.write('A1', 'Its\na bum\nwrap',           text_format)
worksheet.write('B1', 'http://stackoverflow.com/',  link_format)

workbook.close()

Output:

According to the official documentation for Formatting of the Dataframe headers:

Pandas writes the dataframe header with a default cell format. Since it is a cell format it cannot be overridden using set_row(). If you wish to use your own format for the headings then the best approach is to turn off the automatic header from Pandas and write your own.

So, we turn off the automatic header from Pandas and write our own. The defined header_format should be applied to each column header in the df_input and written to the worksheet. The following is customized to your requirement and a similar example is shown in the official docs.

# Turn off the default header and skip one row to allow us to insert a
# user defined header.
df_input.to_excel(writer, sheet_name='Inputs', startrow=1, header=False)

# Get the xlsxwriter workbook and worksheet objects.
workbook  = writer.book
worksheet = writer.sheets['Inputs']

# Add a header format.
header_format = workbook.add_format({
    'bold': True,
    'text_wrap': True})

# Write the column headers with the defined format.
for col_num, value in enumerate(df_input.columns.values):
    worksheet.write(0, col_num + 1, value, header_format)

To set the text wrap format for the entire column you need to add the format object to a set_column() call. Something like this:

writer.sheets['For PDF'].set_column(col_idx, col_idx, column_width, text_format)

Set the column_width to None if you don't want to specify the column width. Also, your current code seems to be auto fitting the column widths. Having very wide columns, to the width of the string, will mean that the text won't/won't need to wrap.

Update: added example.

import pandas as pd


# Create a Pandas dataframe from some data.
df2 = pd.DataFrame({'Control name': ['foo', 'bar', 'baz'],
                    'Rationale': [
                        'some long sentence ' * 4,
                        'some longer sentence ' * 6,
                        'hello ' * 10]})

# Create a Pandas Excel writer using XlsxWriter as the engine.
writer = pd.ExcelWriter('pandas_wrap.xlsx', engine='xlsxwriter')

# Convert the dataframe to an XlsxWriter Excel object.
df2.to_excel(writer, sheet_name='For PDF')


# Get the xlsxwriter workbook and worksheet objects.
workbook  = writer.book
worksheet = writer.sheets['For PDF']

# Add a format.
text_format = workbook.add_format({'text_wrap' : True})

# Resize columns for clarity and add formatting to column C.
worksheet.set_column(1, 1, 20)
worksheet.set_column(2, 2, 20, text_format)

# Close the Pandas Excel writer and output the Excel file.
writer.save()

Output:

You can use pandas with the xlsxwriter engine (the default).

You need to create a format object by calling the workbook.add_format() method as outlined in the xlsxwriter docs (link here).

Once you've used pandas.DataFrame.to_excel(), you can add the format using worksheet.set_column(). An example of this can be found in the xlsxwriter docs (link here).

I've provided a fully reproducible example below with the expected output.

import pandas as pd

df = pd.DataFrame({'Ticket': ['a','b','c','d'],
                  'Category': [2,1,4,3]})


writer = pd.ExcelWriter('Trial Version.xlsx', engine='xlsxwriter')
df.to_excel(writer, sheet_name='Sheet1', index=False)
workbook=writer.book
worksheet = writer.sheets['Sheet1']

format = workbook.add_format({'text_wrap': True})

# Setting the format but not setting the column width.
worksheet.set_column('A:B', None, format)

writer.save()

Expected Output:

As noted in the XlsxWriter docs, DataFrame formatting cannot be overwritten using set_row(). The easiest way to change the formatting of a DataFrame header is to overwrite the header with individual cell entries, overwriting the value and the format of each cell:

import pandas as pd
import xlsxwriter

df = pd.DataFrame({'this is a very long header that should wrap': ['a2', 'a3', 'a4'],
                   'header2': [1, 2, 3],
                   'header3': [4, 5, 6]})

writer = pd.ExcelWriter('test.xlsx', engine='xlsxwriter')
df.to_excel(writer, sheet_name='Sheet1', startrow=1, header=False)

workbook  = writer.book
worksheet = writer.sheets['Sheet1']
header_format = workbook.add_format({'bold': True, 'text_wrap': True, 'valign': 'top'})

# Overwrite both the value and the format of each header cell
for col_num, value in enumerate(df.columns.values):
    worksheet.write(0, col_num + 1, value, header_format)

workbook.close()

The code above will produce the following: