"And to these two gems - who still attempt to climb 'mama mountain', smother me with kisses, and make every day the most memorable adventure... being your mom is the greatest privilege of my life", followed by a red heart emoji.
Meghan also appears to use her new post to reveal one of her children's favourite foods.
She added, "I, too, "love you more than all the stars in all the sky, all the raindrops, and all the salt on all the French fries in all the world."
The Duke and Duchess of Sussex have largely made the decision to keep Archie and Lilibet, affectionately known as Lili, out of the spotlight - although Meghan has treated fans to various pictures since her return to Instagram back in January.
The doting mum uploaded a new picture of Archie earlier this week to mark his sixth birthday on May 6.
Accompanying by a picture of Archie looking at a sunset with his back to the camera, Meghan wrote: "Our son. Our sun. Happy 6th birthday to Archie! Thank you for all of the love, prayers, and warm wishes for our sweet boy. He’s six! Where did the time go?
"(And for all of you who came to celebrate with us at his party last weekend, thank you for making his birthday so incredibly special [love heart emoji])"
14 PerFlyer