Yes you should get a letter within a week or so and it will tell you the details. I don't know if it says approved but it will give you a date to call usually Tuesday's and you should get your check on Friday.
You should receive a letter in the mail telling you all the details when you are finally approved. You may also receive a phone call to confirm your information, that's when you'll know the wheels are turning. These people can be notoriously overworked though so it may take awhile. Good luck!