North West, Kim Kardashian West, Saint West & Kanye West.Picture: Instagram

Kim Kardashian West is a "very hands-on" mother, getting up in the night with baby Chicago to help bond with her new daughter.

The 'Keeping Up With The Kardashians' star and her husband Kanye West welcomed their third child via a surrogate last week, and the 37-year-old star is being a "very hands-on" mother to her new daughter.

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A source told Us Weekly magazine: "Kim gets up for everything, in the middle of the night, especially in the first week. It's really important they bond with the baby. Kim's a very hands-on mom. Baby is settling in beautifully. Chi is sleeping a ton for now."

An insider also revealed that Kim was the first person to have skin-to-skin contact with Chicago - an important process in bonding with any new baby - after she was born, followed by rapper Kanye, 40.

Chicago was born weighing 7lbs 6oz on January 15.

Kim - who is also mother to four-year-old daughter North and two-year-old son Saint - chose to have her third child via a surrogate due to health complications during her previous pregnancies.

Announcing the arrival, Kim said: "Kanye and I are happy to announce the arrival of our healthy, beautiful baby girl. We are incredibly grateful to our surrogate who made our dreams come true with the greatest gift one could give and to our wonderful doctors and nurses for their special care. North and Saint are especially thrilled to welcome their baby sister."

While the couple have not given a reason for naming their daughter Chicago, a source has claimed they chose the name in tribute to the city where Kanye grew up.

Kim's sister Khloe Kardashian revealed on social media that Chicago's nickname is Chi, which is pronounced, "shy".

Khloe tweeted: "I LOOOOOOOOOOVE her name ... hey Chi (shy)"