Amber Rudd said the Government will embark on a “phased approach” but did not give further details.
The process could cost the taxpayer £100 million a year and require another 3,000 Home Office staff, the Liberal Democrats said, while the Migration Observatory at the University of Oxford has said the process would be a “formidable task” that could amount to the equivalent of around 140 years of work at recent rates of processing.
Responding to a question from Brexit select committee chairman Hilary Benn in the Commons, Ms Rudd said: “There will be a need to have some sort of documentation, he is entirely right, but we are not going to set it out yet.
“We are going to do it in a phased approach, to ensure that we use all the technology advantages that we are increasingly able to harness, to ensure that all immigration is carefully handled.”
Lib Dem foreign affairs spokesman Tom Brake said the processing would add “roughly 10% to the Home Office workload” costing at least another £100m a year and requiring 3,000 extra staff.
Meanwhile Ms Rudd said foreign students are likely to remain in the Government’s target to cut immigration to the tens of thousands amid growing clamour for them to be separated.
Over the weekend, Foreign Secretary Boris Johnson backed excluding them from the overall numbers - a stance also taken by Chancellor Philip Hammond.
Ms Rudd said: “Students play an important role in contributing to the economy and are most welcome in the UK.
“The internationally-recognised definition of a migrant is someone coming here for over 12 months, so they are likely to stay within that definition, although I’m aware there are different views on this matter.”
When asked by Home Affairs select committee chairwoman Yvette Cooper whether students should be taken out of the overall target, Ms Rudd replied: “There are different views on this.
“The definition that I referred to was for international students, which is held by the ONS, which is for over 12 months, they represent an immigrant and are therefore part of the numbers.”
The Home Secretary also stressed that following Brexit the UK will have greater control over its borders.
She said: “One thing is for certain, though, is that when we do leave the European Union we will have more control over immigration from the European Union and will be making sure the immigration that we do get from the European Union gets the right balance of attracting the type of people who can really boost the UK businesses that need it.”