The broader NSE index ended 1.07% higher at 11,568.35, while the benchmark BSE index finished 1.17% higher at 39,052.06.
UK Prime Minister Boris Johnson said that Britain and the European Union had agreed a "great" new Brexit deal and urged lawmakers to approve it at the weekend.
Meanwhile, the corporate earnings season for the September quarter has already seen companies such as Hindustan Unilever and Wipro beat expectations.
Earlier in the day, TVS Motor Company Ltd reported a quarterly profit that comfortably beat estimates, sending its shares up as much as 9.5% and finally settling at 6.83%.