Val Willcox, antenatal teacher at the National Childbirth Trust (NCT), said kangaroo care, where the baby is cuddled on a parent's bare chest, is one of the best ways of bonding with a baby soon after their birth.
The birthing expert said: "If Meghan's able to do skin-to-skin, we know that that really helps with the baby adjusting to life outside of the womb.
"It also helps the mother, if Meghan is intending to breastfeed.
"Lots of early skin-to-skin between the mother and baby can really help with getting breastfeeding off to a good start."
The concept, which is often used for premature babies, will also help Harry develop his own bond with his child, and is beneficial for the baby too.
"Harry can also do skin-to-skin with the baby if he wants. It will help calm and soothe the baby and help the baby regulate their temperature and heart rate," said Ms Willcox.
She added: "I encourage couples to spend a lot of time cuddling and holding their baby.
"You can't spoil a newborn baby.
"Rather than Harry thinking that the only thing he can do is changing dirty nappies, actually, if he spends a lot of time soothing and comforting and cuddling his baby, it really helps build that early initial bond between the baby and the baby's primary caregivers."
Ms Willcox advised the duke to help wind the baby and to ensure both he and the duchess get plenty of rest and nutritious food.
"It's about dividing the load between them of caring for the baby and making sure each other gets the opportunity to rest," she said.
"Harry can make sure that Meghan gets good stuff to eat and drink, as well as making sure that he's feeding himself as well - probably a bit easier if you're a member of the royal family.
"You've probably got a bit more help around you than some of us get."
Encouraging the new royal parents to take the time out to cuddle their baby, she said: "If you're sat one afternoon with your baby on your chest while your baby is having a little nap and you're just sitting counting every eyelash and every hair on the baby's head, that's absolutely fine.
"That's part of getting to know your baby."