Robert Shepherd, six, and Christianne, seven, of Horbury, West Yorkshire, were killed by fumes from a faulty boiler in Corfu in 2006.
Their parents Neil Shepherd and Sharon Wood were refused funding as lawyers are not normally required at inquests.
But after a meeting with David Cameron they have now been granted legal aid.
Mr Shepherd said the family were "pleased and relieved" by the news.
He added: "We are now in a position to be able to concentrate on getting the full facts of Christi and Bobby's deaths out in the public without the added worry of cost."
Mrs Wood said there was "an overwhelming public interest for the lessons of our tragedy to be learned so that no other family suffers as we have".
The two children were overcome by fumes while on holiday at the Louis Corcyra Beach Hotel in Gouvia, with their father and his partner Ruth Beatson.
Mr Shepherd and Ms Beatson were both left in a coma as a result, but survived.
Tour operator Thomas Cook was cleared of responsibility in relation to the deaths. The manager of the hotel and two other members of staff were convicted of manslaughter.
The family met Prime Minister David Cameron, legal aid minister Shailesh Vara and MP Mary Creagh in April.
In a statement, Mr Vara said: "This is a very tragic case in which two young children lost their lives and my deepest sympathies are with the family, with whom the prime minister and I recently met.
"Questions remain unanswered and I have therefore authorised legal aid for representation at the inquest to hopefully provide much-needed answers."
Ms Creagh, who organised the meeting after raising it in the House of Commons during Prime Minister's Question Time in March, described the decision as "a big victory" and said the family should "never have been put in this position".
A full inquest is due to take place next year.
A family whose children died from carbon monoxide poisoning while on holiday has been granted legal aid for an inquest after it was rejected.