A tweet from 20th Century Fox's corporate communications account confirmed that the filmmaker "has agreed to make AVATAR 2 and 3 as his next films (sic)".
A further update on the Fox social networking site added: "Cameron, who always viewed AVATAR as creation of new world and mythology, will begin writing in early 2011 with eye towards late 2011 start."
Cameron had earlier revealed that he was considering making another movie before embarking on the next Avatar films.
Sony's Angelina Jolie-led Cleopatra was a project Cameron had expressed an interest in helming.
Avatar 2 will be released in December 2014, followed by Avatar 3 in December 2015.