Tristan and Blake Barrass, aged 13 and 14, were killed by their parents Sarah Barrass and Brandon Machin, who are half brother and sister.
The boys were strangled then suffocated with plastic bags just a day after the couple's bid to poison them failed, a court heard last year.
Barrass, 36, and Machin, 40, hatched the plan over fears their secret sexual relationship would result in their six children being taken away. Both are serving life sentences for the murders as well as plotting to kill the other four youngsters.
The house stood as a permanent reminder of the tragedy for traumatised neighbours and residents for nearly two years, but it has now been torn down by a social housing company who owns the plot.
Following lengthy consultations, approval to demolish the house was given to owners Sanctuary Housing in July last year.
The firm said the decision to knock down the house was made in order to "help the local community move forward".
An open space with a memorial tree will replace the property in Gregg House Road in the Shiregreen area of Sheffield.
A spokesperson for Sanctuary Group said: “The decision has been taken as we believe it is the right option to help the local community move forward and because it will allow us to create a suitable memorial to the events that occurred.
"An open space will be created when the property is removed, and the space will include a memorial tree to provide a subtle reminder of the tragic events that occurred at the address.”
The surviving members of the family have been informed of the plan and support it, the firm said.
Locals expressed their relief the house has been demolished.
Nikki Walker said: “The house isn’t far from me and I’m glad to see it gone after what those vile creatures did to those poor lads.”
Lisa Kirk Taylor said: “I live about 10 houses up and every time I pass that house it brings it all back what happened and it’s really upsetting. It’s nice what they are doing but no matter what it will never be forgotten what happened there even though the house is gone.”
Carys Dixon said: “This will hopefully be a very lovely memorial garden for not only siblings and family members, but also the community that was rocked by such a horrible tragedy.”
Sheffield Crown Court last year heard the horrific circumstances surrounding Blake and Tristan's murders.
Barrass and Machin spent nine days hatching their plan after becoming concerned their children would be taken away by social services.
They tried to poison four of their children on May 23 by forcing them to take a cocktail of drugs including prescribed ADHD medication.
Barrass expected them to die during the night and even made 'light-hearted' Facebook posts about the children catching a sickness bug.
When the children survived the night Barrass summoned Machin from his home nearby back to the property.
They grabbed Blake and Tristan, with Machin strangling Blake whilst Barrass strangled Tristan using a dressing gown cord, it was heard.
The pair then swapped victims and placed black bin liners over their heads, which is how the boys were found on bunk beds.
Police, medics and an air ambulance rushed to the property at 7.30am on May 24 and attended to the critically injured teens.
Tristan was pronounced dead at 09:14am that morning and Blake died 12 minutes later at 09.26.am.
The other four children, all under the age of 13 and who cannot be named for legal reasons, were taken to hospital and released later that day.
Barrass and Machin both admitted two counts of murder, five of attempted murder and one of conspiracy to murder six children.
They were jailed for life with a minimum term of 35 years in November last year.
Since the killings, the house where the murders took place has remained empty.
Speaking when the decision was made, Sanctuary Housing operations director Daren Nowlan said: “We have taken our time over making this decision as we have been sensitive to the huge impact of this event both locally and nationally.
"We believe the decision we have made is the right one to help the community move forward and are committed to ensuring a permanent memorial is created so the two young lives lost are never forgotten."