He said: "I was so touched when I heard her story that I just wanted to do something.
"I wasn't in the UK at the time, so I recorded a message and sent it to her straight away. She's a very brave girl."
However, Abigail - who is holding her 16th birthday party two years early because doctors have told her she has just weeks to live - may not be able to make the gig because she is so ill.
Her mother Maria told The Sun newspaper: "She was delighted and really pleased. We put it on the iPod so Abigail could watch it when she woke up.
"He said Happy Birthday in the message and asked if she wanted to get to a gig - and he said he could sort it out. We don't know if Abi will make it to a show though because she only has days or weeks left."
Apart from seeing Ed, Abigail also wants to fly in a hot air balloon and have a custard pie and jelly fight.
She said: "I'm determined to enjoy the time I have left with family and friends."
For her party she had planned to charge a £2 entrance fee so she could complete her 'bucket list' before she dies.