The 30-share Sensex ended up 215 points at 19,889 and the 50-share Nifty ended up 72 points at 6,044.
Foreign institutional investors were net buyers of 8.97 billion rupees of stocks on Monday, taking the 2013 net buying to a total of $12.17 billion, provisional exchange data showed.
The broader markets underperformed the benchmarks. The BSE midcap index gained 0.8% and the smallcap index rose 0.6%.
Meanwhile, Asian markets edged higher with several markets closing at multi week highs. The Nikkei average jumped 3.6% to14,180 its highest closing level since June 2008 with exporters leading the gains.
Hong Kong shares ended at multi-week highs in choppy trades investors braced for a slew of economic data from China that could offer fresh clues on the recovery in the world's second-largest economy.
The Hang Seng Index closed up 0.6% at 23,047 and the Shanghai Composite Index closed up 0.2%.
In Europe, markets edged higher on the back of strong earnings from major banks. Germany’s DAX, France’s CAC and FTSE were up 0.3-0.6% each.
Back home, all sectoral indices on the BSE ended in the green. FMCG, Bankex, Realty, Auto, Capital Goods were the top gainers up 1-2%
Nifty ends below 5,950 on RBI's hawkish stance
Markets end higher led by index heavyweights
Nifty hits 3-month high, ends shy of 6,000
Govt yet to make up mind on Rangarajan panel plans
Rupee falls to near one-week low