The install file downloaded from the App Store will vary based on the device and what thinning is done to your app. An ad hoc distribution .ipa file will give an estimate of how big the install file from the App Store will be. Archive your app in Xcode, then make an ad hoc distribution. If you turn off app thinning while making this file you'll see the biggest your install file could be. If you turn on app thinning and generate all the variations of .ipa files you'll see all the different install file sizes.
To see an even more accurate answer to this question, submit your app to TestFlight. In the TestFlight app on your devices you can see the size of the app by checking the app details. Check it on multiple devices, it will vary if the app thinning process considers your devices sufficiently different and uses different assets from your app archive.
Below is my original answer:
In Xcode 4: Once your app is ready for distribution, archive the app. In the Organizer, select the Archives tab. Select your app in the left hand column. Select the latest archive in the right hand column. Hit the Share... button in the top section. Save the file as an .ipa. Check file size in the Finder.