Sir Michael Wilshaw urged the government to make it illegal for pupils to have them on school grounds because they were “far too distracting”.
In extreme cases, the ban could lead to court action against parents whose children repeatedly refuse to comply.
He also said that parents who fail to attend parents’ evenings should be fined, and he condemned the ITV show Love Island as a "sad reflection of today’s education system" that showed how "mediocre" English schools had become.
Sir Michael, who led Ofsted until last year and is known for his tough approach to discipline, is a former head teacher.
His comments about cellphones come in the week Culture Secretary Matt Hancock said he admired headmasters who did not allow pupils to use phones at school.
Following a pledge in Emmanuel Macron’s presidential campaign last year, France has passed a law banning students from using cellphones anywhere at school.
Speaking at the Festival of Education at Wellington College in Berkshire, Sir Michael said: "Any sensible head would ban mobile phones. It’s interesting that President Macron is bringing in legislation to ban mobile phones in state schools. We should do the same.
"It’s far too distracting for children. Texting, sexting - mobile phones go off in classrooms, disrupting lessons. Ban them. If children want to use a phone in an emergency, they can use the school phone."
Ofsted boss Amanda Spielman is also throwing her weight behind school leaders who ban the devices, telling the festival that the place of smartphones in the classroom was "dubious at best".
However, Sir Michael is the first to suggest that a ban should be enshrined in law.
He also risked angering teachers by saying some “lazy” ones "knock off at 3.30", adding: "There is an education establishment out there that doesn’t like change, doesn’t like people like me saying, 'You’ve got some people in your own profession who are lazy and feckless and you need to get rid of them'.”
He suggested that the profession would say that all teachers were hard-working and professional, but he insisted: "They’re not. I’ve been teaching for 43 years. Not all teachers are professional, not all teachers are committed, not all teachers do their best."
However, Dr Mary Bousted, joint general secretary of the National Education Union, said: "Teachers work more unpaid overtime than any other profession."
Sir Michael also laid into Love Island, admitting that he had only watched it for a few minutes.
The reality show, which has been mocked for the ignorance of some of its contestants, is the perfect example of how schools are failing youngsters, Sir Michael said.
He added: "I saw five minutes of it the other day and was absolutely appalled. It is a sad reflection of today’s education system.
"It’s a mediocre system, and it is foolish to claim otherwise. We are not doing enough about the long tail of underachievement."
In addition, he claimed it was "outrageous" that more than half of parents at some schools did not attend parents’ evenings - and called for offenders to be fined.
He said part of the reason some schools were falling behind was that parents didn’t care or support their children.
He said this attitude was more common in white British communities than among migrant families, adding: "Even the poorest parents can turn up to a parent’s evening." - Daily Mail