Lianne Smith has been sentenced to 30 years in prison for the murder of her children in a Spanish hotel room in 2010, a judicial official said.
The 45-year-old British mother was found guilty in June after she admitted smothering 11-month-old Daniel and five-year-old Rebecca with a plastic bag at the Miramar Hotel on the Costa Brava in May 2010.
In a written sentence issued to the media on Tuesday, Judge Adolfo Garcia Morales jailed Smith for 15 years for each of the murders.
Smith has been seeking an acquittal, claiming she was in a state of "psychiatric disturbance" and suffering insurmountable fear when the tragedy happened.
But the jury rejected her claim that she was "totally disturbed" or she was so scared she could not be expected to act in any other way when she committed the murders.
Judge Garcia Morales said he was imposing the minimum sentence for murder because he considered that, although responsible for her actions, Smith was suffering a degree of "mental disturbance" when she committed the crimes.
He wrote: "The jury stressed that this mental disturbance was not as important as the defence had argued.
"This was based on facts such as several suicide attempts made by Smith, a statement she gave during which she appeared normal and did not make any significant mistakes as she described what had happened and how it happened, the composition of several coherent notes, and calculations she made in order to pay what she believed she still owed to the hotel."
The judge also dismissed the defence's claim that Smith had been suffering "insurmountable fear" when she murdered her children because she feared British social services would take them away from her.
He wrote: "It would have been consequent with insurmountable fear if she had attacked or even killed the members of English social services who she felt were threatening to take her children away.
"It is illogical that out of insurmountable fear of losing her children she decided to kill them."
After the verdict was given, Victor Pillado Quintas, for the prosecution, asked for her to be jailed for a total of 34 years.
Rejecting Smith's claim that she was in a psychotic state when she murdered her children, the jury foreman said: "The defendant admitted during the trial that she was fully conscious of what she was doing and knew it was wrong."
Pillado Quintas has previously described the killings as "horrid, vile and despicable".
Speaking outside the courthouse after the guilty verdict, he said: "Justice has been done, these were abominable crimes."
The murders took place shortly after Smith's partner, Martin Smith, was arrested in Barcelona by Spanish police acting on a European arrest warrant.
The family had been living in Spain since 2007 after fleeing Lichfield, Staffordshire, because Smith's eldest daughter by her first husband accused Mr Smith of raping her.
In December 2010, Martin Smith was found guilty at Manchester Crown Court of using hypnosis, bullying and violence to groom and sexually abuse Sarah Richardson, who has waived her right to anonymity.
Last January, the 46-year-old was found hanged in his cell at Strangeways Prison in Manchester.
Jenifer Lahoz Abos, for the defence, asked for a maximum sentence of three-and-a-half years in prison.
She asked the judge to consider Smith's admission to police that she killed her children as a mitigating factor.
After her partner was deported to the UK, Smith thought British social services were in Spain to take the children away from her.
Lloret de Mar was the first place she visited when she arrived in Spain, so she took her children to hide there.
The court heard that after spending two days with Daniel and Rebecca at the Miramar, Smith suffocated them as they slept on the night of May 17 2010.
First she smothered her son with a plastic bag and immediately afterwards she used the same bag to kill her daughter.
Smith then tried to take her own life by cutting herself with razors, covering her head with a plastic bag, hanging herself with telephone cable and drowning in a bath.
After failing in her suicide attempts, she went down to reception at 1.30pm the following day and asked for police and an ambulance to be called.
She let an officer from Lloret de Mar local police into the room, pointed to a bed where the dead children lay covered by sheets and confessed to killing them.
The jury was shown footage of the interview police conducted with Smith in the room next door to where the murders took place.
In the harrowing video, she said her family had reached the "end of the road" after Martin Smith was arrested and deported.
She said: "I gave my children a three-day holiday, a perfect holiday, we were very, very happy.
"We came here (to Lloret) with nothing, we had left everything again.
"This was the end of the road, I knew my children would be taken back to England.
"So I know it's not right to take another life, but I felt I was in a corner and my intention was for me and my children to go."
The children were buried in Lloret de Mar cemetery after a small private funeral in the town's Sant Roma church.