The classical singer, 42, who performed for the Queen on many occasions, said it was a “huge honour” to be selected to record the new national anthem for the first time since the death of Queen Elizabeth II.
She said: “I have only the fondest memories singing the national anthem for Her Majesty The Queen, memories I will always cherish.
“While my heart is heavy with grief, singing this today for the first time is a huge honour and was sung with the belief that King Charles III’s reign will be happy and glorious.”
Jenkins, who recorded the song in a small church in a remote area of Sussex, had a moment of silence and prayer before “singing from the heart”.
The lyrics include the lines: “God save our gracious King, long live our noble King, God save the King.”
The anthem closed the extended World At One programme on BBC Radio 4 on Friday.
Jenkins has performed at a number of royal occasions including the Queen’s 90th birthday celebrations at Windsor Castle in 2016.
She also took part in the celebrations over the Queen’s Platinum Jubilee weekend, including performing at a special outdoor concert at Sandringham alongside the Military Wives Choirs, and appeared in the Songs of Praise: Platinum Jubilee Special.
She was among the stars on the bill for the recent A Gallop Through History event, which was broadcast on ITV and featured stars like Tom Cruise, Dame Helen Mirren and comedian Omid Djalili.
Following the news of the Queen’s death age 96 on Thursday, Jenkins shared a series of pictures of her greeting the monarch.
She wrote: “On this heartbreaking day, my thoughts, prayers and deepest condolences are with King Charles, the Royal family and with my fellow Brits & commonwealth members around the world.
“Your Majesty, thank you for all you have given. You have been a selfless constant in our lives, knowing just what to say in our darkest hours.
“You inspired us with your dignity, your duty and your grace. I am proud to have lived during your reign, honoured to have sung for you and privileged to have known you.”