The rally was mainly driven by a good show in the European and other Asian markets including jump in the U.S. markets on Friday.
The broad-based NSE Nifty 50 went up by 81.65 points or 0.78% to 10,536.60.
The BSE index surged 294.71 points to close on 34,300.47 while the broader NSE index finished on 10,539.75, gaining 84.80 points.
Brokers said sustained buying by domestic institutional investors ahead of inflation data improved the market sentiment.
The Sensex touched a high of 34,351.34 points and a low of 34,115.12 points during the intra-day trade.More news: IS leader al-Baghdadi suffering from deteriorating health
Tata Steel February 9 had reported a five-fold rise in consolidated net profit at Rs 1,135.92 crore for the third quarter ended December 31.
Domestic institutional investors bought shares worth a net Rs 588.42 crore while foreign portfolio investors sold shares worth a net Rs 1351.70 crore on Friday, provisional data showed. Both indices were higher than Friday's close by almost 0.7%.
The rupee recovered by 15 paise to 64.25 against the dollar in opening trade today on fresh selling of the USA currency by exporters and banks amid a higher opening in domestic equity markets.
SBI, however, dropped 2.67 per cent following poor quarterly results.
Tata Steel, Aurobindo Pharma, UPL, Yes Bank and IndusInd Bank were the main movers on Nifty gaining nearly 4%, while HCL Technology, SBI, Bharat Petroleum Corporation Ltd, Bharti Infratel and Tech Mahindra were the top losing stocks, falling nearly 2%. BSE Information Technology (-0.43%) and teck (-0.34%) were the only losers. "European indices like FTSE 100, DAX and CAC 40 traded in the green", he added.
India's stocks, bonds and currency markets are closed on Tuesday for a public holiday.