In last seven days, the index has gained 1,359.23 points, its longest winning run since February.
Meanwhile, NSE Nifty reclaimed the crucial 8,300-mark.
Global cues were firm on reports that Greece has given its creditors new proposals on reforming bailout, fuelling hopes of averting a default and possible exit from the euro zone.
"A better-than-forecasted monsoon has reignited the optimism amongst market participants that a rate-cut by the RBI may be a possibility, if the monsoon trend sustains," said Hitesh Agrawal, Head Research of Reliance Securities.
More From This Section
The 30-share BSE index resumed higher and remained in the positive terrain throughout the day. It hit an intra-day high of 27,782.31 before ending at 27,730.21, a steep rise of 414.04 points or 1.52 per cent -- its biggest single day gain since May 8 when it surged by 506.28.
The broader 50-issue NSE Nifty reclaimed 8,300-mark to hit a intra-day peak at 8,369.45 and settled at 8,353.10, showing a significant rise of 128.15 points or 1.56 per cent.
Top gainers among Sensex included Axis Bank, which surged 3.62 per cent and ICICI Bank zoomed 3.46 per cent.
Globally, Asian markets closed higher while European markets were higher in their afternoon trade.