Disability groups such as Radar, which has long campaigned for portable support packages, have welcomed the decision.
It would allow an individual to retain their entitlement to free personal care when they move to another local authority until a new community care assessment can be undertaken.
The amendment was promoted by the crossbench peer Commission Baroness Campbell of Surbiton, who is a commissioner on the Equality and Human Rights.
“It is vital that those with critical-plus needs receive seamless support if and when they move home to be near relatives,” she said.
A government consultation on the bill closed yesterday.
Critics continued to lambast the government over its costings and planned implementation date of 1 October. But their amendments on the costings and the planned implementation date were either withdrawn or not moved.
Conservative shadow minister for health Earl Howe said: “These rushed decisions are almost bound to impact adversely upon council residents. We cannot predict in what ways because that will depend on the budgets that are cut, or the new charges that are levied. Even then, councils will still be groping about in the dark prior to 1 October as regards the costs of implementation.”
The bill will continue its committee stage in the House of Lords on 1 March.