The Go 2 School initiative started simultaneously in the capital Mogadishu and in the main cities of Somaliland and Puntland.
It’s being supported by the UN children’s agency, Unicef, at a cost of $117m (£75m).
After two decades of civil war, aid agencies say Somalia’s formal education system has almost completely collapsed.
School enrolment rates are among the lowest in the world. Only four out 10 Somali children currently attend school.
Girls are particularly badly affected. Only one in three are at schools in south and central Somalia, where the militant Islamist group Al-Shabab still controls many areas.
‘Lost generations’
Unicef says the project will give a quarter of young people currently out of education a chance to learn.
“Education is the key to the future of Somalia,” Unicef’s Somalia Representative Sikander Khan said.
In June the Somali prime minister, Abdi Farah Shirdon, promised that his government would give education the same priority as defence and security.
“We have lost two generations of children to war,” Somalia’s education minister Maryam Qasim told the BBC, “the Somali child cannot wait for another generation.”
She said she was undeterred by the security threat from Al-Shabab saying that education would prevent children joining the militant group.
Al-Shabab was driven out of Mogadishu in August 2011 and other main towns after that but still carries out attacks and suicide bombings.
President Mohamud took office a year ago in a UN-backed bid to end two decades of violence.