It supports a previous decision by the High Court that it was in the public interest for the government to carry out its policies.
Under the scheme, some of those entering the UK illegally will be flown to Rwanda to apply for asylum there.
Campaigners were trying to stop the flight before a full hearing on whether the policy is lawful next month.
The charity Detention Action and the PCS union that represents some Border Force staff, who were among the groups who brought the case, said they were disappointed by the decision.
