You can delete your account from Yahoo’s website. Yahoo warns that your account might not be recoverable if you modify your mind, but you’re welcome to make a new account within the future.
Open Yahoo's page and enter your username. Click Next.
Enter your password. If you've got an Account Key found out, Yahoo will send a message to your mobile phone to authenticate you.
Read the text on the page titled "Before continuing, please consider the following information." It details what you'll lose once you delete your Yahoo Mail account. Press Continue.
Enter your email address another time into the field provided.
Select Yes, terminate this account.