One shows Prince George transfixed by a blue morpho butterfly, which has landed on his dad's hand , while a second shows him with his mother and father, staring at butterflies above their heads.
In a statement Prince William and Kate thanked people for their 'warm and generous good wishes'.
The couple said: "We would like to take this opportunity on George's first birthday to thank everyone over the last year, wherever we have met them, both at home and overseas, for their warm and generous good wishes to George and our family."
The Duke and Duchess are expected to hold a birthday party for the young prince today (Tuesday) at their Kensington Palace apartment.
Prince George was first revealed to the public on the steps of St Mary's hospital in London on 23 July 2013 and we've all watched him grow from a babe in arms to a dashing toddler since then.
An image of Prince George was released on Sunday and the new pictures published today complete the set. In the first of the new photos, Prince George can be seen pointing and gazing intently at the butterfly on Prince William's hand.
The Duchess of Cambridge proudly cuddles her son, keeping a firm grip around his waist, just in case the inquisitive boy should make a grab for it.
After all, on his first public engagement in New Zealand back in April, George unwittingly managed to make a little girl cry by snatching her toy from her.
The second photograph shows young family in the 'Sensational Butterflies' exhibition at the Natural History Museum, in London, as several dozen live butterflies flutter around them.
Kate is wearing a summery £475 'Budding Hearts' tea-dress by designer Suzannah, which she has worn previously on public occasions - complete with drool stain from the royal baby.
George, who, like his mother is becoming something of a trend setter, is wearing blue and white stripped dungarees and a navy top by French label Petit Bateau, which sold out within minutes of another picture from the same set being released at the weekend.
The Duchess was determined to ensure that one of their patronages would benefit from the occasion of Prince George's first birthday, and chose to visit the Natural History Museum' s pop-up tropical house, full of live, free-flying butterflies and moths. She became patron of the museum in April last year.
The exhibition, which runs until September, was opened up especially for the Cambridges and their team earlier this month but, says one closely involved in the proceedings, things didn't entirely run to plan.
As it was early morning, the butterflies, which normally swarm around visitors, needed time to warm up, and it was 'touch and go' as to whether the shoot would work.
Fortunately a blue morpho butterfly from South America landed in front of the curious prince and with a click, the carefree shot was captured for posterity.
Sir Michael Dixon, Director of the Natural History Museum said of the visit: "It was a real pleasure to host our Patron and her family earlier this month.
"They seemed to enjoy their visit, wandering through the tropical plants as brightly coloured butterflies took flight around them.
"It was delightful to see Prince George's first experience of the Natural History Museum and I look forward to welcoming them again in the future."
According to his parents, George is already 'racing around and opening doors' at their Kensington Palace apartment, in advance of many of his peers. He has a fine set of lungs on him, makes bath-time 'quite painful' but adores his 'best buddy', Lupo the spaniel.
One friend said: "Like most new parents they are just in awe of this little man they have created. He really is the apple of their eye."
The couple plan to celebrate George's birthday today with a low-key tea party for family and friends at Kensington palace. Michael and Carole Middleton – both extremely hands-on grandparents – will attend, alongside Auntie Pippa and Uncle James.
Unfortunately his royal grandparents Prince Charles and the Duchess of Cornwall are in Scotland on official duties.
But the Queen – who is now the first monarch for more than a century to have three living heirs - has no public engagements in her diary so might pop in to wish her great-grandson a very happy birthday.
More:Baby's First Year
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