Finance Minister Nirmala Sitharaman said the effective corporate tax rate would be lowered to around 25pc from 30pc and scrapped the minimum alternative tax for domestic companies.
Governments and central banks around the world have been loosening monetary and fiscal policies to revive economic growth hurt mainly by the ongoing US-China trade war and weak consumer demand.
India's moves are the latest in a raft of measures from the government to lift the economy after growth hit a six-year low in the April-June period, mainly dragged by a slump in private investment.
"The measures announced by the finance minister this morning can be described as a 'New Deal' for the Indian economy," said VK Vijayakumar, chief investment strategist at Geojit Financial Services.
"The psychological stimulus from this ... will be higher than the fiscal stimulus."
Economists believe that the cuts would make India competitive for investment, as it brings corporate tax rates on a par with other Asian economies.
Reserve Bank of India Governor Shaktikanta Das said the moves augur "extremely well" for the economy.
However, Sitharaman said total taxation revenue loss due to the cuts would be about $20.5 billion, raising concerns that the government may not be able to meet its fiscal deficit target for 2019-20 at a time when tax revenue collections are already weak.
Speculation that the government may have to borrow more to meet its expenditure needs for the year led to a spike in benchmark 10-year bond yields to a 2-1/2-month high.
The broader NSE index jumped as much as 5.9pc to 11,333.55, while the benchmark BSE index jumped 5.8pc to 38,182.36. Both indexes were set to finish the week about 2pc higher.
The rupee rose as much as 0.9pc to 70.68 against the dollar, its strongest level since Aug. 9.
Top lenders HDFC Bank Ltd and ICICI Bank Ltd soared nearly 10pc each, sending the Nifty Bank index up 8.8pc.
"The markets have been asking for a big fiscal stimulus and the government has delivered," said Rusmik Oza, head of fundamental research at Kotak Securities in Mumbai.
Corporate earnings may see an almost 12pc jump in the next quarter for full tax paying companies due to the cut, and the markets can go up nearly 10pc, Oza said, adding that foreign investors would cheer these measures.
The Nifty Auto index jumped 12.4pc, its sharpest intraday climb since July 2011, with Eicher Motors Ltd surging 24pc.
IT firms dipped as the rupee firmed, with Tata Consultancy Services Ltd slipping 1.7pc.