Gates says GDP per capita figures, adjusted for inflation to 2005 dollars, show that many countries such as China, India, Brazil and even Botswana that were once considered poor now have growing economies.
And in Africa, a place the Microsoft co-founder says is all too often dismissed as hopeless, life expectancy has risen since the 1960s despite the HIV epidemic. Also, more children are going to school and fewer people are hungry.
"I am optimistic enough about this that I am willing to make a prediction," he said. "By 2035, there will be almost no poor countries left in the world."
Gates also argues against claims that foreign aid is wasteful because it is too expensive, because it is stolen by corrupt officials receiving it or because countries who receive it become dependent on it.
He says that in Norway, the world's most generous donor of foreign aid, the amount of its budget that goes to foreign aid is only 3 percent. In the U.S., it's less than 1 percent, or about $30 billion per year, of which $11 billion goes to vaccines, bed nets and other health causes.
Measles vaccinations, eradicating smallpox, controlling tuberculosis in China and a plan to eliminate polio in Latin America are all public health efforts achieved with aid funding.
"Health aid is a phenomenal investment," he writes. "When I look at how many fewer children are dying than 30 years ago, and how many people are living longer and healthier lives, I get quite optimistic about the future."
His wife, Melinda, wrote a section of the letter dispelling the myth that saving lives worldwide will lead to overpopulation. She points to countries such as Brazil where both child mortality and birth rates have declined.
When more children survive, she says, parents have smaller families.
"The planet does not thrive when the sickest are allowed to die off, but rather when they are able to improve their lives," she says. "Human beings are not machines. We don't reproduce mindlessly. We make decisions based on the circumstances we face."
The Seattle, Wash.-based Bill & Melinda Gates Foundation is the world's largest charitable foundation and has made $28.3 billion in grant payments since its inception 13 years ago.