Mr McAvoy beat Christine Blower, a national executive member of the National Union of Teachers, by a majority of more than 17,000 votes on a 29.8 per cent turnout.
Ms Blower had said that more industrial action was likely in classrooms if she won the contest.
Mr McAvoy said: "It is a great honour to be general secretary for a third successive term. Members have demonstrated their support for the union as a campaigning but not a militant organisation - an organisation which speaks for the whole profession and not for a political faction."
Earlier this year, he warned members that Ms Blower had "a political and revolutionary platform that she and those who control her seek to impose on members".
Last week, he said in an advertisement that she was supported by extreme left-wing groups such as Militant, the Socialist Teachers' Alliance and the Socialist Workers' Party.
Ms Blower said that she was not controlled by any group and was not a member of a political party.
In 1994, Mr McAvoy defeated another left-wing challenger, Mary Hufford, by a majority of only 1,500 on a turn-out of 38.9 per cent.
This year, he received 39,245 votes compared with his opponent's 22,183.
Ms Blower said she was disappointed by the low turn-out. "I think I fought a positive campaign," she said. "I regret that Doug McAvoy's style of campaign was negative."
She believed that this may have raised doubts in many members' minds about the point of voting.Reuse content