If I had discovered that on a professional basis my approach would be removing the joist entirely, checking where the ingress of water was and trying to fix it. Then replacing it with a new joist. That would be a few hours work depending on the difficulty involved in detecting and fixing the leak.
If you just want it to last another 10-20 years bang another joist next to it and cover it up before it bothers you!
If I had discovered that on a professional basis my approach would be removing the joist entirely, checking where the ingress of water was and trying to fix it. Then replacing it with a new joist. That would be a few hours work depending on the difficulty involved in detecting and fixing the leak.
If you just want it to last another 10-20 years bang another joist next to it and cover it up before it bothers you!