Menon and Singh will call on Bhutanese King Jigme Khesar Namgyel Wangchuck and meet newly elected Prime Minister Tshering Tobgay, said a statement issued by the Ministry of Foreign Affairs here.
They will also meet Foreign Minister Rinzin Dorje and the Opposition leader Dr Pema Gyamtsho, it added.
Tobgay's People's Democratic Party won a landslide victory in Bhutan's second national elections held on July 13. The PDP defeated Druk Phuensum Tshogpa party by winning 32 seats out of the 47 in the National Assembly.
Their tour, the statement said, is part of the traditional exchange of high-level visits between the two countries.
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Singh had said last week that India and Bhutan share a unique relationship which has always been characterised by mutual trust and confidence.
"We are working closely with the new government of Bhutan to continue to consolidate our privileged partnership," she said, adding "unfortunate technical lapse" resulted in the disruption of the supply of subsidised gas and kerosene.
Singh said Prime Minister Manmohan Singh has invited his Bhutanese counterpart to visit India.