The Sensex scaled 319 points at 40,790, while the Nifty jumped 89 points to surpass 12,000 amid heavy buying.
Heavyweight Reliance Industries touched a 52-week high of Rs1,571, up 4% after foreign broking house Credit Suisse raised its target price to Rs1,400.
RIL's infocomm arm Jio announced its plan to hike tariffs, following peers Bharti Airtel and Vodafone Idea on Tuesday.
Shares of Vodafone Idea continued extending massive gains, up by 17% currently.
Sectorally, all indices traded in the green with media and pharma stocks shining the most.
Top gainers included Reliance Industries, Airtel, and Sun Pharma, while losers included Eicher Motors and Bharti Infratel.
Meanwhile, the rupee recovered all its losses and is flat at 71.72/$ on Wednesday.
The US FOMC is expected to release its minutes of the October meet later today.