The You're A Lady star passed away on Friday following a battle with brain cancer.
He was ordained following special permission from the Archbishop of Canterbury, Justin Welby.
Skellern began ordination training - a dream since he was nine years old - almost three years ago.
He was then diagnosed with an inoperable brain tumour, but was encouraged to continue with his work.
Following his official ordination in October, he said: "For about a week I hung in this abyss and I just grabbed God.
"It was like that for about a week and then God closed the ground beneath me and I became resigned and happy and I have been like that ever since."
His family said on Friday: "Peter's creativity in art, comedy and music stand as his legacy to love and laughter.
"The love he brought to us will continue to be shared with everyone through his music. We will miss him with all our hearts."
Born in Bury, Lancashire, before later moving to Cornwall, Mr Skellern began his musical career at his local church and studied at Guildhall School of Music and Drama.
He began recording in the 1970s, releasing 14 albums and collaborating with fellow musician, Sir Richard Stilgoe.