The grey pony hunter is named Frozen and arrived in Los Angeles from the Netherlands earlier this week.
Sources with knowledge of the deal said it would have cost between $7,000 and $10,000 to ship the pony to the US on top of the $200,000 sale price.
The 17-year-old gelding is currently in the middle of a 14-day quarantine and will be moved to a barn closer to 22-year-old Kylie’s Calabasas home when it is complete.
Breeder Stal Wilten confirmed the deal in an Instagram post on Thursday in which he referenced the Kylie Cosmetics mogul and which included a photo of Frozen.
He wrote: ‘#ThrowbackThursday goes to the most famous pony of them all, Frozen. We got news he has landed in LA and is living the life with a sweet little girl named Stormi.
‘@KylieJenner, in true fashion, made sure her daughter had the most precious pony out there.
‘We can’t wait to see pictures of Stormi and Frozen.’
At 12 hands, Frozen is large for a first pony and unusually advanced for a beginner’s ride. But a source told DailyMail.com that Wilten has previously sent ponies to LA for celebrity riders.
The source said: ‘Lots of celebrities import horses from the Wiltens or have purchased from their bloodlines – Kaley Cuoco, Jessica Springsteen and Jennifer Gates among them.’
The insider added: ‘Frozen will stay in quarantine for 14 days now so Stormi most likely doesn’t know he’s arrived yet. He’s a very famous pony for a very famous little girl.’
News of the new arrival comes at the end of a tumultuous week for the Kardashian-Jenner clan, which began on Sunday with Kanye West’s first presidential rally.
During the rally in Charleston, South Carolina, he burst into tears as he told how he and wife Kim Kardashian, 39, had considered aborting eldest daughter North, now seven.
West said: ‘In the Bible, it says, “Thou shall not kill.” I remember that my girlfriend called me screaming and crying, and I was just thinking — because at that time I was a rapper I was out there, [had] different girlfriends and everything — and she said, “I’m pregnant.” And I said, “Yes!” And then I said, “Uh oh”.
‘She was crying… and for one month and two months and three months, we talked about her not having this child. She had the pills in her hand.’
He then claimed that a vision from God led to them going ahead with the pregnancy. West said: ‘I’m in the apartment where my wife was actually robbed, and I have my laptop up and I have all of my creative ideas, I’ve got my shoes, I’ve got my next song cover… and the screen went black and white.
‘And God said, ‘If you f*** with my vision I’m gonna f*** with yours.” And I called my wife and she said, “We’re gonna have this baby,” and I said “We’re gonna have this child.”’
West has been staying at his 4,000-acre ranch just outside the tiny Wyoming town of Cody since Sunday and has been spotted filming a music video on the ranch, as well as taking a trip to Walmart with friend Damon Dash.
But he has also been on a series of Twitter rants, accusing Kim of having an affair with rapper Meek Mill and saying he wanted a divorce.
He used another Tweet to call his mother-in-law Kris Jenner, 64, ‘Kris Jong-Un’ – a reference to the North Korean dictator.
West also said he wanted Kris and ‘that calmye’ [sic] – thought to mean her boyfriend Corey Gamble – nowhere near his children and claimed the Kardashian matriarch is refusing to take his calls.
He has also released a succession of cryptic messages insisting that none of his children will appear in Playboy magazine – unlike their mother, who has.