How long will it take to learn chords?

Obviously, there are many factors to consider. But here are a few guidelines I can give you. 

Dont believe the claims by some authors that you can learn chords in 24 hours, or 10 days, or 6 weeks. Actually, if you read their claims literally, they are telling the truth. I can teach you how to play chords in 3 hours (that's how long my workshops usually are), but that only means that I can show you how to play chords and suggest ways for you to study them. You could feasibly learn chords in a few days (maybe 24 days at one hour a day for a total of 24 hours!) but that doesn't mean you can play songs proficiently. But with consistent practice and within a few weeks, you will be able to easily play many of your songs in basic chord format. 

If you play piano proficiently, then you already have the coordination skills to play the melody in your right hand and the chords in your left. Chords will feel natural in your hands because you already play them, you just may not know it because they aren't called out on classical pieces and most piano solo arrangements. Learning basic chords won't take long, but you'll be spending your time learning to embellish songs and playing styles such as blues or Latin or pop. 

Many of my students who've never played before learn to play basic chord piano within just a few weeks and become proficient within a year. Within a couple of years, they can play fairly sophisticated songs, such as jazz or standards.