MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.3 per cent, building on its bounce from a two-month low touched on February 9.
Japan's Nikkei rose 1.0 per cent to three-week highs.
On Wall Street, the S&P 500 advanced 1.18 per cent on Monday helped by fall in US bond yields.
The 10-year US Treasuries yield eased to 2.864 per cent, dropping further from its four-year peak of 2.957 per cent touched on February 21, driven by month-end buying as well as position adjustments ahead of Mr Powell's testimony.
Mr Powell's debut appearance is seen as critical for financial markets at a time when many investors are nervous about the Fed's policy normalisation following years of stimulus after the financial crisis almost a decade ago.
Many expect the Fed to raise interest rates three to four times this year, as policy makers look to prevent an overheating of the economy especially as growth is set to get another boost from the Trump administration's tax cuts and spending plans.
Yet, investors are worried rising dollar funding costs could bode ill for potential borrowers, including US home buyers and some emerging market companies.
MSCI's gauge of equity market performance in 47 countries gained 0.82 per cent on Monday, rising above its February 16 high to hit it a three week top.
"The combination of low interest, low inflation and strong economic growth, the best combination for markets that also kept market volatilities low, is coming to an end," said Mutsumi Kagawa, chief global strategist at Rakuten Securities,
He said that while corporate earnings will likely remain strong for a while longer, underpinning stocks, market volatility will be higher.
In the currency market, the euro traded at $1.23145, off its three-year high of $1.2556 hit earlier this month.
The dollar traded at 106.98 yen , stabilising for now above its 15-month low of 105.545 set on Feb 16.
Fed funds rate futures were almost fully pricing in a rate hike at the Fed's next policy meeting on March 20-21.
Oil prices held firm at three-week highs, supported by strong US demand and comments from Saudi Arabia that it would continue to curb production in line with OPEC-led efforts.
US West Texas Intermediate futures fetched $64.00, up slightly on Tuesday, after hitting a 20-day high of $64.24 the previous day.