Well, there are easier ways. Use floodgates!
Start by digging a small room near the bank of the river. Then tunnel a passage from the river to your well. In my current fortress I carved downward stairs for about three z-levels on the way to my to the well room, which was a basically a 10x10 room one level below my well. Depending on the distance between river and well, you might want to make this passage a couple or more squares wide, as it can take some time for water to flow from the source and fill up the room.
Obviously, you build your well above the room filled with water. I put a lever in that room as well. When everything else is ready, I place a floodgate or two at the far end of tunnel, facing the river, and connect it/them to the lever.
Once everything is in place, I build channel on the surface level from the river to the floodgates, if you understand what I mean. This is easier, safer, and just as effective as opening the gates and digging that last tunnel square to the river. Once the channels are built, the water flows into them, you open your floodgates, and after a while -- e voila -- your well is ready!
Remember that a well requires at least 3 squares of water under it to work.
Finally, in my experience, you don't really need the floodgates. I've left them open this entire time and so far the water in the room under my well hasn't risen above 7. I'm not 100% sure, but I kinda doubt it can flood the level above it.