Sushma Swaraj will first meet Mr Oli, who has had strained relations with the Indian leadership, before taking up other engagements.
Her visit will be the first diplomatic engagement after elections in Nepal catapulted the alliance of the Communist Party of Nepal (Unified Marxist-Leninist) and CPN (Maoist Centre) to power.
Ms Swaraj will also call on outgoing Prime Minister Sher Bahadur Deuba and Maoist leader Pushpa Kamal Dahal 'Prachanda'.
The timing of the visit ahead of the government formation underlines India's attempts to improve its ties with Mr Oli, who is seen as close to China, and the CPN-UML, diplomats say.
Relations between India and Nepal became acrimonious in 2016. Mr Oli was sharply critical of New Delhi's policy towards Nepal after his government was toppled in July that year.
Mr Oli also turned against India following the 2015 blockade in Nepal that triggered an economic and humanitarian crisis.
Mr Oli, as Prime Minister in 2015, signed several agreements with China, including trade and transit deals, with a view to end India's monopoly over the Nepali market.
The diplomatic engagement is taking place though the new Prime Minister is yet to be sworn in Nepal.
Soon after the election results were announced, Prime Minister Narendra Modi reached out to Mr Oli and showed eagerness to welcome him in India.
Experts believe that the Sushma Swaraj trip was a "conciliatory" move by New Delhi to mend ties with Kathmandu.