Nadarajah Nithiyakumar, 41, attacked his daughter Pavinya, aged 19 months, and three-year-old son Nigash at the family home in Aldborough Road North, Ilford, east London, on April 26.
The children's mother, named locally as Nisa, was in the shower at the time of the killings and alerted police.
Pavinya was pronounced dead at the scene while Nigash was rushed to hospital in Whitechapel but he also died.
Their father was taken to hospital for treatment for knife wounds.
Upon being discharged, the shop worker was charged with murdering the children.
In a police interview, Nithiyakumar accepted he had killed his daughter and son with a knife.
He said he had been depressed and while working in a shop, customers had "upset him".
He had thought about killing himself, but considered it would "ruin the children's lives and they would go off the rails", a court previously heard.
On Thursday, the defendant appeared before Mrs Justice Cutts at the Old Bailey.
He pleaded guilty to two counts of manslaughter by diminished responsibility, which was accepted by the prosecution.
He will be sentenced later.
The children's mother wept in court as the defendant pleaded guilty to manslaughter but not guilty to murder.
She was supported by her sister, who was also tearful, and assisted by a Tamil interpreter.
Prosecutor Duncan Atkinson QC told the court psychiatrists had agreed the defendant suffered from a delusional disorder.
He said the case was "on any view of the very greatest seriousness" and had been considered with great care by the prosecution.
"It is clear from the unanimous opinion of very experienced psychiatrists that this defendant was at the time of these offences suffering from a delusional disorder," Mr Atkinson said.
"It was one from which he had suffered for some time, for the best part of 10 years. with very little indication and very little treatment."
The prosecutor said it had been considered by one expert "remarkable he was able to function for as long as he did".
Mr Atkinson added: "It was clear it was that disorder that led him to kill his children."
The court heard Nithiyakumar has no previous history of violence.
There is no other explanation for his behaviour "other than that which he accepted he did", the lawyer said.
Mr Atkinson said: "In those circumstances the Crown took the view it is appropriate to accept the plea of manslaughter by reason of diminished responsibility."
He asked the murder charges be left on the court file.
Mrs Justice Cutts agreed and adjourned the sentencing until December 10.
She said she will consider a hospital order and whether Nithiyakumar poses a danger to the public at that hearing.
The judge told Nithiyakumar: "I'm not going to sentence you today. I need further information from the doctors and to hear from them evidence in person before I can decide what the appropriate sentence should be."
Nithiyakumar was sent back to the medium secure mental health centre in east London where he has been treated.
In May, at the funeral of her children, heartbroken mum Nisa reportedly buried them in a shared coffin with their favourite teddy bear.
A small funeral was held amid the coronavirus lockdown, with a burial ceremony at Greenford Park Ceremony in west London.
Nisa reportedly told them: "Don’t worry daughter, your brother will now guide you. Look after each other."
Nisa, who was aged 35 at the time, left photographs of Nigish and Pavinya at their graveside taken when they were babies, as that's how she wants them to be remembered, reports said.
The children's uncle, Gopala Krishnan, told the Daily Mail at the time: "It was a very sad day. We are devastated by what happened and are still trying to come to terms with it. None of this makes any sense."
Following the dad's arrest, Detective chief inspector Vicky Tunstall said the "ending of these innocent young lives is extraordinarily tragic".
She added that the "effects of this crime are reverberating throughout the local community" but reassured people that there was "no cause for the community to be fearful or alarmed".
Thank you for reaching out to us. We are happy to receive your opinion and request. If you need advert or sponsored post, We’re excited you’re considering advertising or sponsoring a post on our blog. Your support is what keeps us going. With the current trend, it’s very obvious content marketing is the way to go. Banner advertising and trying to get customers through Google Adwords may get you customers but it has been proven beyond doubt that Content Marketing has more lasting benefits.
We offer majorly two types of advertising:
1. Sponsored Posts: If you are really interested in publishing a sponsored post or a press release, video content, advertorial or any other kind of sponsored post, then you are at the right place.
WHAT KIND OF SPONSORED POSTS DO WE ACCEPT?
Generally, a sponsored post can be any of the following:
Press release
Advertorial
Video content
Article
Interview
This kind of post is usually written to promote you or your business. However, we do prefer posts that naturally flow with the site’s general content. This means we can also promote artists, songs, cosmetic products and things that you love of all products or services.
DURATION & BONUSES
Every sponsored article will remain live on the site as long as this website exists. The duration is indefinite! Again, we will share your post on our social media channels and our email subscribers too will get to read your article. You’re exposing your article to our: Twitter followers, Facebook fans and other social networks.
We will also try as much as possible to optimize your post for search engines as well.
Submission of Materials : Sponsored post should be well written in English language and all materials must be delivered via electronic medium. All sponsored posts must be delivered via electronic version, either on disk or e-mail on Microsoft Word unless otherwise noted.
PRICING
The price largely depends on if you’re writing the content or we’re to do that. But if your are writing the content, it is $60 per article.
2. Banner Advertising: We also offer banner advertising in various sizes and of course, our prices are flexible. you may choose to for the weekly rate or simply buy your desired number of impressions.
Technical Details And Pricing
Banner Size 300 X 250 pixels : Appears on the home page and below all pages on the site.
Banner Size 728 X 90 pixels: Appears on the top right Corner of the homepage and all pages on the site.
Large rectangle Banner Size (336x280) : Appears on the home page and below all pages on the site.
Small square (200x200) : Appears on the right side of the home page and all pages on the site.
Half page (300x600) : Appears on the right side of the home page and all pages on the site.
Portrait (300x1050) : Appears on the right side of the home page and all pages on the site.
Billboard (970x250) : Appears on the home page.
Submission of Materials : Banner ads can be in jpeg, jpg and gif format. All materials must be deliverd via electronic medium. All ads must be delivered via electronic version, either on disk or e-mail in the ordered pixel dimensions unless otherwise noted.
For advertising offers, send an email with your name,company, website, country and advert or sponsored post you want to appear on our website to advert @ alexa. ng
Normally, we should respond within 48 hours.