Tokyo ended the morning session 0.1 percent higher, while Sydney was up 0.6 percent.
Where inflation remains closer to the Fed's 2.0% to 2.5% target range is on the year-over-year readings.
Fed officials also cut their forecast for inflation, one of the last indicators to really pick up momentum in recent years.
Meanwhile, the rate of inflation over the past 12 months has slowed to 1.9% in May from 2.7% just in February.
But beyond the announcement of another rate hike, anticipation surrounds the possibility that the Fed could signal policy shifts in a statement it will issue, in updated economic forecasts and in a news conference with Chair Janet Yellen.
The Federal Reserve raised rates Wednesday afternoon at the conclusion of its two-day meeting, signifying a stamp of approval on America's economic recovery from the nation's highest fiscal policymakers. "That points to a flatter yield curve". With US unemployment at a 16-year low of 4.3% and the US economy still growing, it would be a major surprise if the Fed does not announce a rate hike. The remainder will be reinvested.
The Fed will start shedding Treasuries at the rate of $6 billion per month, and will increase that pace by $6 billion per month every quarter for a year, at which point the rate will reach a maximum level of $30 billion per month. The initial cap will be set at $10 billion a month: $6 billion from Treasuries and $4 billion from mortgage-backed securities. Several Fed officials have said publicly they expect the runoff program to continue until the balance sheet declines to about $2 trillion to $2.5 trillion.
In Asia, markets reacted in a fairly benign fashion to some better than expected Chinese industrial production data for May, and retail sales numbers that were slightly down on the April figures. The Fed lowered its inflation forecast for 2017 but expects inflation to hit its 2% target over the medium term. And it's a sign that the central bank believes the US economy is on solid ground.
The UK unemployment rate remained unchanged at the lowest level since 1975, but wage growth remained subdued squeezing household spending.
Significantly, and possibly in reaction to weaker-than-expected CPI data for May released earlier that same day, the FOMC said it was now "monitoring inflation developments closely".
Although it did not provide a precise date for the start of its balance sheet reduction, the FOMC said it would begin to gradually roll-off a fixed amount of assets each month. Tech stocks climbed the most among industry groups, rebounding from their Monday drop for a second session.
Many economists have been anticipating one more interest rate increase from the Fed before the end of 2017 and will be looking for confirmation of that strategy. As of Friday, June 9, the fed funds market was pricing in a 96% chance that the Fed will hike rates by 0.25% at this week's meeting.