Janet Yellen, who took over as the bank's chair at the start of the month, will testify to a House of Representatives committee later in the day on the state of the economy and the course of monetary policy.
Sydney rose 0.62%, or 32.4 points, to close at 5,254.5 and Seoul added 0.46%, or 8.76 points, to 1,932.06.
Hong Kong jumped 1.78%, or 383.72 points, to 21,962.98 and Shanghai rose 0.84%, or 17.60 points, to 2,103.67.
Tokyo was closed for a public holiday.
The latest gains indicate traders' nerves may have settled after the turmoil seen earlier February when the Fed said it would further reduce its bond-buying scheme and US and Chinese manufacturing data came in below forecast.
Markets brushed off a second straight set of poor jobs data on Friday, with some blaming severe winter weather for the weak growth, while also pointing to positive news such as a rise in labour force participation.
Ms Yellen's testimony will be pored over to see if she gives any indication that the central bank will slow down its stimulus tapering. In December, the Fed said it would cut its monthly purchases by $10 billion to $65 billion. It then announced a similar move this month, sending markets spinning.
Credit Agricole said investors would be keen to see if she maintains a doveish bias on the drawdown, against the backdrop of a more hawkish policymaking committee in the Fed.
"While we do not expect any major deviations from the Fed's current outlook, her interpretation of the recent softening in US data will be an important driver for markets," it said.
"Against this backdrop, the extent she views the recent soft patch in data as a function of weather-related effects (and other seasonal distortions) could support policy normalisation," it said.
Wall Street provided a positive lead for Asia. The Dow edged up 0.05% on Monday, the S&P 500 gained 0.16% and the Nasdaq rose 0.54%.
In forex trade the euro ticked up to $1.3659 and 139.69 yen compared with $1.3642 and 139.46 yen in New York.
The dollar was at 102.25 yen against 102.18 yen.
Oil prices were mixed. New York's main futures contract, West Texas Intermediate for delivery in March, was down six cents to $100 a barrel in afternoon trade. Brent North Sea crude for March delivery was up two cents to $108.65.
Gold fetched $1,283.73 an ounce at 0810 GMT compared with $1,272.60 late Monday.
In other markets, Taipei rose 0.46%, or 38.61 points, to 8,430.56. Taiwan Semiconductor Manufacturing Co added 1.46% to T$104.5 while leading chip design house MediaTek was 2.2% higher at T$419.
Wellington rose 0.33%, or 15.83 points, to 4,848.88.
Fletcher Building was up 1.89% at NZ$9.15 and Telecom gained 0.63% to NZ$2.3w9.
Manila was 1.06% higher, adding 63.78 points to 6,106.03.
Bank of the Philippine Islands rose 0.23% to 87.60 pesos, SM Investments added 0.79% to 700.50 pesos and BDO Unibank gained 1.14% to 79.90 pesos.