WAR is literally "wins above replacement." Typically (as in the case with FanGraphs), a replacement level team will win 30% of its games. For an entire season, that comes out to 48.6 wins. So if WAR is doing what it is purported to do, a teams WAR for a season added to 48.6 should be a good estimate of the number of wins they actually had. This of course leads one to wonder if WAR actually accomplishes this goal, so I decided to do some research to check it out.
I used the WAR value for each season and each team from 2002-2008 (the only full seasons that I had access to through FanGraphs). This gives 7 years and 30 teams for 210 data points. I took each team's WAR, added 48.6, and compared that to the number of games they actually won. Keep in mind that, unlike some stats like Win Shares, WAR has no adjustments for the number of games the team won. As such this should be a fairly pure estimate. I debated about various ways in which to measure this, but I decided the most straight-forward way was to look at the R2 value.
In the end I came out with an R2 value of .7573. Put simply, WAR accounts for about 76% of the variance. What constitutes a meaningful R2 value differs by context, so I'll let you draw your own conclusions. Beyond the Box Score did a similar study with similar results. They used more data and they took WAR from a different source though.