The four-time Olympic champion pulled clear of American Dathan Ritzenhein in the final mile to coast to victory in a time of one hour and four seconds.
Kenya's Vivian Cheruiyot won the women's race on her half-marathon debut just ahead of countrywoman Priscah Jeptoo.
Farah was the red-hot favourite to complete his hat-trick of titles in the half-marathon, after the successful defence of his 10,000m and 5,000m Olympic titles in Rio last month, and was able to reflect on a near-perfect season.
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"I knew it was going to a hard race today," he told BBC 1. "To be honest I'm knackered. I can hardly talk.
"It's good to finish on a high here. What a year I've had. I just have to go home now and chill out and see the kids."
Farah's time was outside the British record he set last season, at 59mins 23secs, but it hardly mattered as he raced home to rapturous applause from the large crowds that had gathered at the finish.
The 33-year-old endeared himself further to the locals by raising one arm above his head over the closing stages in a homage to former Newcastle United striker Alan Shearer.
He said: ""That celebration was for Shearer. He's a legend. I thought 'why not give something back to the crowd?', there's a lot of Geordies here.
"It was amazing to have so many people cheering for me. That's what drove me on to the end."
The celebration was appreciated by Shearer himself, who posted a picture of Farah's celebration on Twitter alongside the statue of himself that is set to be unveiled at St James' Park: "Love it @Mo_Farah! Apparently they've already built a statue of you to commemorate your hat-trick! ðÂŸÂÂƒ #GreatNorthRun"
Cheruiyot, who won the 5,000m title in Rio, earlier won the women's race by just a second after holding off the 2013 winner Jeptoo.
Scotland's Mark Telford won the men's wheelchair race following a sprint finish from Bret Crossley.