The tot apparently slept through most of the 6,000-mile flight on a private jet from Malawi to London Heathrow. She was then reunited with her new mother - who has not seen her since March - and taken to the singer's Marylebone townhouse.
Mercy apparently reduced her to tears by saying: "Moni, moni mummy," which means "Hello Mummy" in her native Chichewa tongue.
Her new brothers and sisters threw her a welcome tea party before Madonna took the youngster to a special Kabbalah blessing.
And waiting at the centre was the star's former husband Guy Ritchie, who was at the Material Girl's side when she first met Mercy in a Malawi orphanage in 2006.
The family spent an hour at the centre before Mercy and her new mum returned home with Lourdes, while Guy took Rocco and David to his place in Wiltshire. Pals say Madonna will now spend the next week bonding with her new daughter and getting her used to being with her new family.
"(Madonna) has a gentle few days planned ahead, with lots of singing and reading to her new daughter," reveals a friend, who adds: "Mercy has already fallen love with the £2,000 rocking horse Madonna has placed in her bedroom. She can't take her eyes off it."
One person who wasn't around to meet the new arrival was Madonna's love interest Jesus Luz. The 22-year-old model was busy strutting his stuff for Dolce & Gabbana at Milan's menswear presentation.
The Brazilian hunk, whose career has gone stratospheric since he was first linked to the singer, also stars in the Italian fashion house's new ad campaign.