He added there is a "moral duty" to reopen schools next month for all students despite the continued threat from the coronavirus.
Writing for the Mail on Sunday newspaper, Johnson said it was "crucial" for children's welfare, health and future that they return to the classroom full time. "We can do it -- and we will do it. Social justice demands it."
Most UK schoolchildren have been at home since the government imposed coronavirus lockdown measures in March.
“This pandemic isn’t over, and the last thing any of us can afford to do is become complacent,” Johnson wrote. “But now that we know enough to reopen schools to all pupils safely, we have a moral duty to do so.”
Johnson said time spent out of the classroom could lead to lower educational attainment and have a lasting impact on children's future life chances.
"Most painfully of all, the costs of school closure have fallen disproportionately on the most disadvantaged, the very children who need school the most," he wrote.
"Keeping our schools closed a moment longer than absolutely necessary is socially intolerable, economically unsustainable and morally indefensible."
Teachers' unions have voiced concerns over the safety of staff and students when schools reopen.