How long after Implanon removal will my period stop?

There's no way to definitively answer this, as there are so many factors involved regarding your own body, how long you've been on it, etc.

Most likely it will be a few weeks with some tapering down to breakthrough bleeding towards the end. But don't be surprised if it takes 6 months to return to complete regularity. 6 months on a new bc / 6 months off an old bc is generally the rule when it comes to waiting for side effects to fade completely and your body to fully adjust to the difference in hormones.

Good luck!!! Finding the perfect bc is always h e double hockey sticks but there will be something for you. For non-pill, long term usage and menstrual control, I might recommended a hormonal IUD (which usually stops your periods completely or shortens/lightens them significantly). I personally use Nuvaring and I "stack" them so that I skip my period most months and have it at will approx every 3-4 months.
Remember though to always give a new bc 6 months to settle and adjust before giving up on it, unless it's extreme or making you completely miserable! Most side effects and irregularities will fade over that time.

It's impossible to say, unfortunately, as everyone is different.