Parker - who was a singer in The Wanted - passed away in March, 17 months after announcing he had been diagnosed with a brain tumour.
Following the news, Sheeran said he was 'so sad' to hear of the 33-year-old's death, and it has since transpired that the pop star had helped Parker to cover his medical bills.
In an extract from Parker's autobiography Hope, which is due to be posthumously released on 26 May, he labelled the 'Shape of You' singer a 'very special man'.
In the extract, published by The Sun, he wrote: "Pretty much from the moment I was diagnosed, Ed Sheeran reached out to me with an offer to do anything he could to help.
"Ed and I have known each other since he joined The Wanted on our tour bus during a promotion trip in America more than ten years ago. We’ve always run into each other over the years and had a great relationship.
"I've never publicly said this before (and he'll probably be mad that I'm doing it now) but Ed is a very special man - he even helped out with my medical bills when I was seeking other treatment options and having private immunotherapy.
"He didn't need to do any of that, but my wife Kelsey and I are so grateful to him for his support. It meant the world."
Formed in 2009, The Wanted saw Parker star alongside Max George, Siva Kaneswaran, Nathan Sykes and Jay McGuiness on hits like 'Chasing the Sun', 'All Time Low' and 'Glad You Came'.
His former bandmates reacted to the news of his death on Instagram, posting: "Max, Jay, Siva, Nathan and the whole Wanted family are devastated by the tragic and premature loss of our bandmate Tom Parker, who passed away peacefully at lunchtime today surrounded by his family and his bandmates.
"Tom was an amazing husband to Kelsey, and father to Aurelia and Bodhi.
"He was our brother, words can't express the loss and sadness we feel.
"Always and forever in our hearts."
Parker married his wife Kelsey in 2018, and the pair have two children, Aurelia Rose, born in 2019, and Bodhi, born last October.
On Instagram, Kelsey wrote: "Our hearts are broken.
"Tom was the centre of our world. We can't imagine life without his infectious smile and energetic presence.
"We are truly thankful for the outpouring of love and support and ask that we all unite to ensure Tom's light continues to shine for his beautiful children.
"Thank you to everyone who has supported in his care throughout, he fought until the very end. I'm forever proud of you."
If you’ve been affected by any of these issues and want to speak to someone in confidence, contact Macmillan’s Cancer Support Line on 0808 808 00 00, 8am–8pm seven days a week