The UK Court of Appeal upheld on Monday a ruling made June 10 refusing to grant a temporary injunction suspending the first flight, slated for June 14.
Judge Rabinder Singh said the Court of Appeal could not interfere with the original "clear and detailed" judgement, and refused permission for further appeal. A full hearing to determine the legality of the policy as a whole is due in July.
The government says the deportation strategy will undermine people-smuggling networks and stem the flow of migrants risking their lives by crossing the English Channel in small boats from Europe.
Initially, some 37 individuals were scheduled to be removed on the first flight to Rwanda, but the charity Care4Calais said that number has dwindled in the face of legal challenges to just eight.
Human rights group say the policy is inhumane and will put migrants at risk. The UNHCR has said Rwanda, whose own human rights record is under scrutiny, does not have the capacity to process the claims, and there was a risk some could migrants could be returned to countries from which they had fled.
The government has not provided details of those selected for deportation, but charities say they include people fleeing Afghanistan and Syria.
Earlier, Prime Minister Boris Johnson said "It's very important that the criminal gangs who are putting people's lives at risk in the Channel, understand that their business model is going to be broken and is being broken by this government," Johnson told LBC radio.
"They are selling people false hope and luring them into something that is extremely risky and criminal."
The government said the deportation plan would deter the Channel crossings, although more than 3,500 people have reached Britain in small boats since the middle of April when the Rwanda scheme was unveiled, according to government figures
The High Court is separately hearing arguments from Asylum Aid, a refugee charity, which launched a second legal challenge to stop the government flying refugees to Rwanda.
Charlotte Kilroy, a lawyer representing Asylum Aid, said asylum seekers were not given enough time to challenge their deportation, meaning there was a high risk of unlawful and unsafe decisions.
This case is being heard by Jonathan Swift, the same judge who on Friday rejected granting an injunction.