In Gmail, go to the cog icon on the upper right hand of the screen and then select See All Settings

Go to the Accounts and Import tab

Select Add another email address under the Send Mail As... section

Enter the name you wish to show when sending as the address for the name

Enter the email address you want to add as a sending address. If this is an announcement address, untick Treat as an alias.

Click Next step and follow the instructions of inputting the code from the email you receive.

If preferred, tick the option Reply from the same address to which the message was sent so you don't have to worry about switching to the correct address each time. (See screenshot below)

You should now be able to switch to the new address in the Compose window (See screenshot below)