def sign_execute_order(order_params, private_key):
    """
    Function to execute the order request by signing the transaction generated from the create order function.
    Execution of this function is as follows::

        sign_execute_order(order_params=signable_params, private_key=eth_private_key)

    The expected return result for this function is as follows::

        {
            'signatures': {
                'fill_groups': {},
                'fills': {},
                'makes': {
                    '392cd607-27ed-4702-880d-eab8d67a4201': '0x5f62c585e0978454cc89aa3b86d3ea6afbd80fc521....'
                }
            }
        }

    :param order_params: The parameters generated by the create function that now require signing.
    :type order_params: dict
    :param private_key: The Ethereum private key to sign the deposit parameters.
    :type private_key: str
    :return: Dictionary of the signed transaction to place an order on the Switcheo Order Book.
    """
    execute_params = {
        'signatures': {
            'fill_groups': sign_txn_array(messages=order_params['fill_groups'], private_key=private_key),
            'fills': {},
            'makes': sign_txn_array(messages=order_params['makes'], private_key=private_key),
        }
    }
    return execute_params