The three children were placed in foster care after the couple's arrest by counter-terrorism officers in 2015.
Mr Justice Cobb said he was suspicious the parents were going to areas controlled by so-called Islamic State.
But he said their "attitude" had "genuinely changed" and he concluded that the children should return home.
The judge, who is based in the Family Division of the High Court, said he was also satisfied that the couple will meet their children's needs.
He said evidence showed that being in the family home will be in their best interests.
Details of the case have emerged in rulings published by Mr Justice Cobb following private family court hearings in Leeds.
The judge did not identify the couple. He said they were from London but lived in the north-east of England.
Council social workers had asked him to make decisions about where the children should live.
The couple were arrested while in a car with their children at the Eurotunnel terminal in Folkestone, Kent, during the summer of 2015.
They had not been accused of any terrorism-related offences as a result of their arrest, but had faced fraud charges.
The couple had told police that they were travelling to Germany to visit relatives, although the man admitted that he had been "drawn into radical extreme thinking".
Mr Justice Cobb said evidence caused him "very considerable concern" and he said he was "suspicious" that the couple had been heading for areas of the Middle East controlled by IS.
But he said suspicion was not enough.
Mr Justice Cobb said he had been told how the couple had co-operated with social services after the children were taken into foster care.
The father said he accepted that things he had said before were "not appropriate" and "not a true expression of Islam", and the mother had accepted that views she expressed "were wrong".
"I am sufficiently satisfied... that the attitudes of these parents have genuinely changed," said Mr Justice Cobb.
"I am satisfied from the information placed before me that these parents [will meet] the needs of these... children in all material respects."
He added: "All relevant considerations point to the conclusion that it is indeed in the best interests of the children that they should [be] at home in the care of their parents."

Total catches of cod, haddock and plaice have been increased, the Scottish government said.
Catches of saithe, whiting and herring will be decreased in line with long-term management plans.
Talks between the EU and Norway agreed the total allowable catch for cod would be 29,189 tonnes, 5% up on 2014.
The increase will give UK fishermen an additional 542 tonnes and Scottish fishermen around 343 tonnes.
A 6% increase in the haddock catch to 40,711 tonnes gives the UK an additional 3,468 tonnes and Scottish fishermen more than 2,500 extra tonnes.
Scottish Fisheries Secretary Richard Lochhead said: "I am pleased there has been an increase in the quota of these key stocks for next year which is in line with the recent scientific advice that the stocks are in good shape.
"It is welcome the agreement has been reached quickly this year compared to the protracted talks last year and will provide certainty for the industry about opportunities in 2015 and avoids any delays to the commencement of fishing in the new year.
"There is much to be done to prepare for the discard ban which starts to come into force for white fish from 2016. This outcome will help these stocks continue to rebuild next year while also helping to minimise discards, and should provide a sound launchpad for establishing the following year's quota under the ban.
"We now look ahead to the crucial December EU fisheries council when we will be highlighting again that our vessels need to retain the number of days they can go to sea as any cut would simply be counterproductive."
UK Fisheries Minister George Eustice said the agreements were an "excellent result for the UK".
He said: "It sees UK fishermen getting a 5% increase in their quota for cod - the second successive rise in annual cod quota in two years. The increase is an encouraging sign that we are achieving our goals; a thriving fishing industry with sustainable fish stocks.
"The deal also saw a 7% rise in North Sea haddock and 15% rise in plaice quotas. This is great news for our fisheries ahead of vital quota negotiations next month where I will be representing UK fishermen."
A Muslim couple arrested over fears that they were heading to Syria for "extremist activities" have won a court fight for the care of their children.
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Early agreement has been reached on North Sea fishing quotas for next year, with an increase in key stocks for Scottish fishermen.