If you are looking to send direct message to your new twitter followers automatically, then these free tools are for you. Use them wisely, do not spam or send messages continuously.
Twitter DMer
Twitter DMer is the simplest tool to send automated direct message to your new twitter followers. Its totally free to use. All you need to do is login to their account through your twitter credentials and set up a message that you would like to send to your new twitter followers.
You cannot send it to your existing followers but it will be automatically send to the new followers.
Social Oomph
Social oomph is another service to send automatic direct messages to your new followers but is slightly more advanced. You have two options, free and professional accounts. You can send DM in free account. Both the account has more features than just sending DM.
Tweet Manager
Using tweet manager you can follow and track twitter users using your desired keywords. It provides more features than simply sending direct messages to new followers. You can look at their videos on the front page to get a detailed idea of how it works.
Along with sending DM to new followers, you also get an option to send mass messages to 1000 or less number of users at once.
