Charles automatically became King following the death of the Queen, but the Accession Council attended by privy counsellors on Saturday morning at the State Apartments of St James’s Palace confirmed his role.
Jenkins, who recorded a version of God Save The King for BBC Radio 4, told ITV’s Good Morning Britain: “We have worked together on a few shared charity interests and the one thing I have always admired is he really cares.
“He has a big heart for the things that I have seen him be involved with and that’s why I think he will be a really wonderful king. I have no doubt about that.”
The classical singer, 42, 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 recorded the song in a small church in a remote area of Sussex and 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.”
Jenkins, who performed for the Queen on many occasions, said: “Looking back at those Platinum Jubilee celebrations, I did not realise that was going to be the last time I was going to sing for her.
“There was a really lovely moment where she was driving around in the car as she left and she was right by the stage… I wanted to curtsy for her and she gave me a little wave, that means so much now.
“I think she was such an inspirational lady to so many of us in different ways… we are all saying the same thing, her sense of duty and service working right until the end, faith at the core of all of her decision making, what an incredible role model.
“To have lived under that and to have seen her incredible reign, I feel very proud.”
Jenkins 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.