The tech tycoon and his wife say they will spend at least £2 billion and want to achieve the goal in their daughter's lifetime.
Money will go towards research into cancer and infectious disease as well as heart and neurological problems.
Speaking on Premier's News Hour, Steve Fouch from the Christian Medical Fellowship said: "It's certainly an ambitious statement that they're going to eradicate all diseases by the end of the 21st century.
"Whether it's achievable... who can say at this stage".
He added that if you look back at medical advances since the start of the twentieth century you can see anything is possible: "We had no antibiotics so most bacterial infections were fatal, we had no treatment for cancers and we had very limited pain control".
Through their philanthropic organisation, the Chan Zuckerberg Initiative, the commitment includes £462 million to fund a new research centre in San Francisco where scientific and medical researchers will work alongside engineers on long-term projects spanning years or even decades.