I have done this. I piece all the blocks in a row across what is the width of my quilt minus borders.
Use batting and backing slightly larger than the row of blocks (same as in a whole quilt). Use your usual method of fixing the 3 layers together.
Then you can machine or hand quilt but do not go right to the edges - leave a good 1/2 inch around the outer edges so that you can join the strips together.
when you are ready to put the strips together, stitch the blocks together with a 1/4 seam. Press as normal - just the top. Trim the batting so that the two edges meet and again use your usual method for joining batting. I stitch my hand and use a zig zag ladder stitch.
I find it easiest to join the back by laying one piece over the other, and then folding the raw edge under and use a very small hem stitch to catch it together. If you have left a fair bit of extra fabric, trim it to a sensible amount before overlapping it.
I hope this makes sense, if you are still not sure, please PM me. It is very easy, but it does leave lots of seams on the backing. It is fun to make the backing of different fabrics so that the quilt becomes reversible.