It can be a long an complicated process, which sadly may result in the app being unavailable for a time.
Since the app is free, and you don't need to worry about supporting paying customers who have purchased the app under your account there is another option (and one I recently used when I sold one on my games to a big publisher)...
Remove the app from sale in your account, and actually delete the app completely from iTunes Connect (this fee's up the name to be re-used). Next get the company who you wish to transfer the app to to set up the app again in their iTunes Connect, and get them to re-upload the binary - yes, the app will need to go through the approval process again, but it'll be back on the App Store a lot sooner than the process that Apple suggest.
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