The Fed's bond-buying program has been a source of liquidity for most Asian and emerging markets.
Shares of IT, teck, oil and gas, banking, capital goods and auto companies firmed up.
Investors also expect the RBI to keep interest rates unchanged in a bid to support growth. India's industrial production contracted 2.1 per cent in November, according to data released after market hours on Friday.
Ahead of the RBI's monetary policy review on January 28, Economic Affairs Secretary Arvind Mayaram has pitched for shifting the policy focus to growth as interest rates do not have a bearing on food inflation. The government is scheduled to release data for retail inflation today.
Shares of companies engaged in natural gas production edged higher after the government notified pricing guidelines on Friday, which will almost double rates of all the fuel produced domestically starting April 1.
The BSE Sensex resumed higher at 20,850.24 and firmed up to cross the 21,000 mark to 21,066.08 before quoting at 21,049.16 at 1030 hrs, a gain of 290.67 points or 1.4 per cent.
The 50-share NSE Nifty on the National Stock Exchange advanced 77.25 points, or 1.25 per cent.
The major BSE Sensex gainers were Infosys (2.92 per cent), * Oil & Natural Gas Corpn (2.89 per cent), ICICI Bank (2.69 per cent), Tata Motors (2.58 per cent), Tata Consultancy Services (2.21 per cent), Reliance Industries (2.20 per cent), Larsen & Toubro Ltd (1.66 per cent), Wipro (1.35 per cent), Axis Bank (1.29 per cent), Hindalco Industries (1.18 per cent) and HDFC (1.14 per cent).
Foreign institutional investors bought shares worth a net Rs 68.16 crore last Friday, according to provisional data from the stock exchanges.
Asian stocks were mixed. Key indices in South Korea and Taiwan were up while those in China, Singapore and Hong Kong were lower. The markets in Japan were closed.