The Home Office has confirmed it will not appeal against the ruling, despite previously indicating it would do so.
Many EU citizens could have faced losing their right to residence if they did not further apply for settled or pre-settled status within five years.
The case was brought by a watchdog for EU citizens' rights after Brexit.
The watchdog Independent Monitoring Authority (IMA) was supported by the European Commission and the3million, a group representing EU citizens in the UK. It said the High Court ruling had "averted a ticking time bomb".
In December, Mr Justice Lane concluded that part of the European Union Settlement Scheme (EUSS) set up by the Home Office to settle EU citizens' immigration status was based on an incorrect interpretation of the withdrawal agreement between the UK and the EU.
The Home Office said the judgement was now law and it was working to implement it "as swiftly as possible".
A spokesman said: "Those with pre-settled status are encouraged to apply for settled status as soon as they are eligible, so they can obtain secure evidence of their right of permanent residence in the UK."
Immigration Minister Robert Jenrick said the scheme had been "a huge success. We've supported millions of people with a connection to the UK to gain status so that they can have the reassurance that they need."
Since 2018, the Home Office has run a two-stage process for EU citizens who wanted to remain in the UK.
This EUSS was set up because the EU's freedom of movement principle had meant many people from within the bloc had never needed permission to be in the UK.
The scheme gave them pre-settled status - a limited right to live and work in the UK which expires if they don't re-apply for full settled status after five years.
But at a High Court hearing in London in November, lawyers for the IMA said the settlement scheme was incompatible with the Brexit withdrawal agreement, because of its effect on some EU citizens and their family members, as well as those from countries in the European Economic Area and the European Free Trade Association.
Robert Palmer KC told the court millions of EU citizens living in the UK risked losing their rights and being treated as "illegal overstayers" as a result.
He said about 2.6 million people were affected - those living in the UK before the end of the transition period in 2020 who were granted pre-settled status.
Under the Home Office's rules, those people would lose their right to lawfully live in the UK unless they made a further application within five years.
Mr Palmer said they would be "exposed to considerable serious consequences affecting their right to live, work and access social security support and housing in the UK, and will be liable to detention and removal".
In his ruling, Mr Justice Lane said that, if the Home Office's interpretation of the law was correct, "a very large number of people face the most serious uncertainty", including possible deportation.
He concluded the Home Office had wrongly interpreted the law.
Campaign group The3million, which represents EU citizens in the UK, welcomed the government's decision not to pursue an appeal, saying EU citizens had been "dealing with uncertainty long enough".
It called on the home secretary to secure EU citizens' residency rights, while taking a "pragmatic approach, to safeguard the rights of vulnerable people", including children, elderly people in care, and victims of domestic abuse.