Transport Secretary Grant Shapps on Monday said the changes - which come into effect on Friday - will mean people "can travel just like in the good old days".
The passenger locator forms require people to fill in travel details, their address in the United Kingdom and their vaccination status.
The announcement came as infections were rising in all four parts of the UK — England, Scotland, Wales and Northern Ireland — for the first time since the end of January.
The number of patients in hospital is also going up. Scientists say many of the new infections in England were a more transmissible sub-variant of the Omicron variant.
"We will continue monitoring and tracking potential new variants, and keep a reserve of measures which can be rapidly deployed if needed to keep us safe," Health Secretary Sajid Javid said.