From 04:00 BST on Friday 23 April, most people who have travelled from India in the last 10 days will be refused entry.
British or Irish passport holders, or people with UK residence rights, will be allowed in but must quarantine in a government-approved hotel for 10 days.
Matt Hancock said there had been 103 UK cases of the India variant.
In a statement to the House of Commons on Monday, the health secretary said the vast majority of the cases of the new variant – officially known as B.1.617 – had been linked to international travel.
He said test samples had been analysed to see if the new variant had any “concerning characteristics” such as greater transmissibility or resistance to treatments and vaccines.
He told MPs: “After studying the data, and on a precautionary basis, we’ve made the difficult but vital decision to add India to the red list.”
Confirming the move in House of Commons, Hancock said that the cases of Indian variant identified in Britain has been majorly due to international travels.
He said that samples of that variant have been analysed to see if the new variant has any “concerning characteristics”, such as greater transmissibility or resistance to treatments and vaccines.
“After studying the data, and on a precautionary basis, we’ve made the difficult but vital decision to add India to the red list,” the minister told MPs.
Earlier in the day, UK Prime Minister Boris Johnson called off his trip to India for the second time amid a massive surge in Covid cases in the country.