The 59-year-old Asquith will take over from Sir James Bevan, who joined the UK's environment agency as chief executive last November, soon after Narendra Modi's first visit to the UK as Prime Minister.
"The Honourable Sir Dominic Asquith KCMG has been appointed British High Commissioner to the Republic of India in succession to Sir James Bevan KCMG, who has transferred to a non-governmental public body. The Honourable Sir Dominic will take up his appointment during March 2016," a UK Foreign and Commonwealth Office statement said.
Sir Dominic has been at the forefront of UK-Libya affairs, having served as ambassador in Tripoli in the past and currently chairman of the Libyan British Business Council.
He holds a number of advisory posts at firms like Dentons LLP, Macro Advisory Partners and Group DF International.
He takes charge in India at a time when India-UK ties are at a high and is expected to be joined in New Delhi by wife and four children.