How to port COMPLETED libgdx game from Android to iOS

A more recent guide on how to accomplish this can be found here:
https://medium.com/@apiric/deploying-your-libgdx-game-to-ios-testflight-163cada0696b

Short version:
Install RoboVM version 2.3.10-SNAPSHOT (link)
Create an Xcode project with the same build id as your Libgdx project
Run the Xcode project on your iPhone/iPad
Create an IOSLauncher.ipa file in Android Studio by typing .gradlew ios:createIPA
Create an “Apple Distribution” signing identity and an “App Store” provisioning profile
Install fastlane (link)
Certify and upload your project using fastlane

There are a couple options, but both are not truly production ready solutions. Options below are 'mostly' working. A few features will not work out of box without some custom handling (networking, sound, and a few others).

• RoboVM (free)
• MonoTouch/IKVM ($299 + Apple licence)

These methods work and are currently the best (easy) solutions available to you.

Note that RoboVM is supported by libGDX out-of-the-box as the default iOS target cross-compiler.

Update:

PS: RoboVM is not permanently free anymore. See here. You get a 30 day trial, then it costs 25$/month minimum.