WASHINGTON—The Federal Reserve showed increasing optimism about the U.S. economy and signaled interest rates would rise at a faster pace than previously projected, as it unanimously approved its second rate increase in a decade.

At the central bank’s last policy meeting of the year on Wednesday, officials said they would nudge up the federal-funds target rate by a quarter percentage point, to between 0.50% and 0.75%. Fed officials pointed to a strengthening labor market nearing full employment and inflation moving more rapidly...