The prize from education charity the Varkey Foundation was created to give more status to the teaching profession, with an Oscars-style awards ceremony in Dubai.
Ms Zafirakou was awarded for her work at London's Alperton Community School, one of the most ethnically diverse, with students from some of Britain's poorest families and many with non-English speaking parents.
Zafirakou came first amongst 30,000 entries, from 173 countries not only for her attitude as an educator, but for her efforts outside the school, raising awareness and being pro-active to help better her students' lives.
She was "overwhelmed" to win the prize, presented by Formula One champion Lewis Hamilton in Dubai.
"I teach arts and textiles and they are powerful subjects, it helps students unlock all of their language barriers", she added.
In a video message, Mrs May said: "You have shown enormous dedication and creativity in your work".
The Dubai-based Varkey Foundation organised the event, the fourth time it has handed out the prize for best teacher.
Ms Zafirakou introduced an "artist in residence", who helps the students on a technical level, but also offers an outlet for what can be challenging and hard home circumstances.
When she reached the top 10, she revealed the hardship faced by students, many of whom come from "crowded homes" and were being forced to "play truant to cook meals".
Mr Woo, the head mathematics teacher at Sydney's Cherrybrook Technology High, was one of the 10 finalists. "So, thank you for all you have done and continue to do".
'What is fantastic, is whatever issues they are having at home, whatever is missing from their life or causing them pain, our school is theirs, ' she told the audience. "That's how phenomenal they are".
She will also have to serve as a global ambassador for the Varkey Foundation. She will also be required to remain working as a classroom teacher for at least five years and will be paid the prize money in instalments.
The nine other finalists in the competition were - Nurten Akkuş (Turkey), Marjorie Brown (South Africa), Luis Gutierrez (Colombia), Jesus Insilada (Philippines), Glenn Lee (United States), Diego Mahfouz Faria Lima (Brazil), Koen Timmers (Belgium), Eddie Woo (Australia), and Barbara Anna Zielonka (Norway).