Active auto correction like in iOS I'm pretty new from Android, just dumped my iOS device.

I find it pretty annoying with this feature missing that is auto correction and auto-complete.

In iOS whenever you misspell a word or type a keyboard key near the desired one, the system will automatically change it to the correct word unless demanded otherwise.

Also the auto complete contains hell of a bigger dictionary.

Do you know of a similar app/setting in Android? It takes me much more time to type in my Android.
Stock keyboard (as well as most 3rd-party keyboard apps) has both auto-correct and auto-completion (a.k.a. "suggestions") built in.  Access the keyboard settings via Settings -> Language &amp; input -> Android keyboard.  From there you can enable and fine-tune the auto correction and suggestion options.