Speaking from St George's Hall - the couple's wedding reception venue - Meghan said: It's magic, its's pretty amazing, and I have the best two guys in the world, so I'm really happy."
The duke cradled his two-day-old son who was wrapped in a traditional white shawl and declared "parenting is amazing".
But how challenging is a first baby?
Here are some questions new parents have found themselves asking:
When do I change my baby's nappy?
Babies need their nappy changing frequently but the amount of nappy changes depends on how sensitive their skin is.
Some babies have delicate skin and need changing as soon as they wet themselves otherwise their skin will become sore.
Parents are warned to not leave babies in wet or dirty nappies for too long because their wee and bacteria in their poo may lead to a nappy rash.
How can I help my baby bond with me?
Bonding with your child may not happen right away as you're adjusting and your newborn is getting used to the world.
Parents are encouraged to have skin contact with their child including holding them close to your chest while you feed or even when cuddling.
Talk to your baby - sing, make noises and speak to them - they love the sound of your voice.
How do I stop my baby crying?
Crying is your baby's way of telling you they need comfort and care.
Sometimes it's easy to work out what they want whether that is food, their nappy changing, a cuddle, or the need to release wind and sleep.
You can comfort your baby by offering a cloth or blanket as a comforter, hold your baby close to you and move around gently as well as talking to them.
The amount babies cry tends to peak at about seven weeks, according to the NHS.
How often should I bathe my newborn?
Three baths a week or fewer are plenty as if you bathe your baby more than that you can dry out your baby’s skin.
Just be sure to wait until the umbilical cord has fallen off before you give him or her a bath.
Why is breastfeeding going wrong?
It can seem like your baby is constantly feeding in the beginning, but gradually you and your baby will get into a pattern and the amount of milk you produce will settle.
The NHS also recommends baby-led feeding - this is when you feed your baby as often as they want and for you to let your baby decide when they have had enough.
How can I tell if my baby is seriously ill?
You know your baby better than anyone else so if their behaviour or appearance is worrying then it's best to see a GP.
Is black or green poop normal?
Yes, so is brown, light yellow and seedy mustard.
How long should my baby sleep for?
If your baby is only sleeping for two or three hours at a time through the night and during the day that is normal.
As your baby grows, they'll sleep for longer at night as they'll gradually start to need fewer night feeds.