Not the latest version. That has some API changes that Reaper has yet to support. Damn, it's an oversight on my part that I didn't put this in to the 64-bit version description as well. Now corrected. I'm sorry for the loss of time.
http://ffmpeg.zeranoe.com/builds/win...in64-shared.7z
That's the one that works. There might be newer ones, but this works(I use it).
Place the DLL files from the BIN directory alongside the Reaper.exe. Check the video preferences to make sure it's not using OS decoding, and you should be good to go.
Your program directory should look like this:
Remember that transcoding is sometimes necessary, though rarely for MP4 and most Quicktime files. Prores though, that's another story.