Campaigners failed in an initial legal bid to halt the removals to the east African country, but have confirmed they will take the case to the Court of Appeal on Monday.
Under the policy, some of those entering the UK illegally will be flown to Rwanda to apply for asylum there.
About 31 people have been told they may be on the first flight.
There will be a full judicial review, where the High Court will hear a challenge to the policy as a whole, before the end of July, it heard.
In his decision, the judge Mr Justice Swift accepted there was a “material public interest” in Home Secretary Priti Patel being able to carry out her policies.
Ms Patel praised his judgement and said the government would go ahead with its plans, while Prime Minister Boris Johnson described the ruling as “welcome news”.
However, campaigners who brought the case expressed concern for the welfare of people set to be “forcibly deported”.
One asylum seeker – an Iranian ex-police commander – who was told he will be deported on Tuesday has said he fears being killed by Iranian agents in Rwanda.
He has been held at a detention centre since arriving in the UK from Turkey in May.
Prince Charles is to represent the Queen in Kigali, the Rwandan capital, at a Commonwealth summit later this month. His office reiterated he remains “politically neutral”.
The government hopes the scheme will discourage asylum seekers from crossing the English Channel, by making it clear many cases will now be dealt with by Rwanda.
More than 10,000 people have made the dangerous sea journey so far this year.
While their application is considered by Rwanda those affected will be given accommodation and support and, if successful, will be able to remain there with up to five years’ access to education and support.