The Sensex resumed higher at 27,427.19 and a touched high of 27,601.06 before quoting at 27,594.37 at 1045 hrs, a rise of 278.20 points or 1.02 per cent.
The 50-share Nifty also gained by 91.00 points 1.11 per cent to 8,315.95 at 1045 hrs.
Major gainers were, Axis Bank by 2.94 per cent, HDFC Bank 2.36 per cent, Coal India 1.89 per cent, Tata Motors 1.62 per cent, SBI 1.52 per cent, Tata Steel 1.51 per cent, ICICI Bank 1.49 per cent, HDFC 1.37 per cent, TCS 1.28 per cent, HUL 1.18 per cent and BHEL 1.12 per cent.
In overseas, Asian markets were trading higher with investors encouraged by signs of a compromise in Greece's debt talks with its creditors.
Key indices in Japan, Hong Kong, Taiwan, Singapore and South Korea were up 0.44 to 1.57 per cent. Chinese stock market was shut today.
Indian stocks is expected to remain volatile during the week as traders roll over positions in the futures & options (F&O) segment from the near month June series to July series. The near month 2015 derivatives contracts expire on Thursday.