The blue-chip NSE Nifty 50 index closed up 1.23% at 11,385.35, highest since Feb. 27.
The S&P BSE Sensex closed 1.26% up at 38,858.32, highest since March 3.
"There are no major triggers on the horizon, this opens up opportunity for traders to ramp up prices of companies which are showing some spark of revival," said Deepak Jasani, head of research, HDFC Securities.
In Mumbai trading, Grasim Industries Ltd finished the session 6.68% higher and was the top gainer on the Nifty 50 index.
The Nifty private bank index <.NIFPVTBNK> closed up 2.2% and the Nifty metal index finished 1.76% higher, helped by a 6.01% rise in miner MOIL Ltd.
"These kind of rallies are speculative and we don't know if it will sustain itself," said Deepak Shenoy, founder and chief executive officer, Capitalmind in Bengaluru.
"If we think about post-COVID, there will be both happiness and disappointment and right now markets only want to expect happiness."
The Nifty realty index <.NIFTYREAL>, which tracks real estate firms, advanced the most and closed 4.04% higher.
The Nifty pharma index inched down 0.12% and was the only sub sector to finish in negative territory on Tuesday.
Shares of Vedanta Ltd closed down 0.9%. During the session, the miner slipped as much as 6.1% after an Indian court refused to allow the reopening of its south Indian copper smelter.
Meanwhile, India continued to see a rise in coronavirus cases and deaths. As of Tuesday, the death toll stood at 51,797 and the number of infections crossed 2.70 million.
By Chandini Monnappa