The 35-year-old crossed the line first after the 3,100-mile, 72-day slog across America, from California to New York.
Mr Brown, who took up endurance running after finding marathons "too easy", flew home to his native Cornwall this week for a rest and to consider his future - but he has already ruled out a return to teaching.
After completing the run in Central Park on Saturday, he said: "A person like me doesn't really fit into the education system."
The decision is likely to come as a huge blow for pupils at his former school, Stoke Climsland primary. Pupils helped organise his flights and accommodation, secure sponsorship and set up his website. The school took on extra supply staff to cover his absence.
Mr Brown was even joined for the last 1,000 miles of the race by Amy, his wife, who teaches at Stoke Climsland. She rode alongside him on a bike.
The couple qualified as teachers together in 2002 and celebrated by cycling from John O'Groats to Lands End. The small village school, of less than 200 pupils, this week declined to discuss Mr Brown's decision to quit. The head, chair of governors and school office refused to comment when contacted by The TES. One villager said: "No-one in the village wants to talk about it."
Mr Brown gorged on his favourite Cornish pasties during the race to build up the necessary calories to complete the gruelling trek, which started in Huntingdon Beach on June 12. The fitness fanatic secured sponsorship from the baker Ginsters who arranged for hundreds of pasties to be flown out during the run.
He said: "I don't consider myself mad. I think people who lead their so-called normal lives are crazy because they don't chase their dreams."
Mr Brown, who hopes to have raised about pound;40,000 for the charity Country Holidays for Inner-City Kids, was a supply teacher but had been working at the school for around two years.
He is now thinking about embarking on a new challenge - a speaking tour.