In a lengthy statement Obama added: :"They are that pitcher on our kid's softball team, that first responder who helps the community after a disaster, that cadet who wants nothing more than to wear the uniform of the country that gave him a chance.
"Kicking them out won't lower the unemployment rate, or lighten anyone else's taxes, or raise anybody's wages."
He said Trump's decision was "self-defeating" and called on Congress to protect the Dreamers "with a sense of moral urgency".
Obama said the decision was "contrary to our spirit, and to common sense".
The Deferred Action for Childhood Arrivals programme, known as DACA, was introduced by President Barack Obama in 2012.
It allowed people who arrived illegally in the US when they were under 16, and have no criminal record, to legally study and work. Their deferral from deportation was renewed every two years.
Many of those children, now known as the "Dreamers," have since been to university, obtained high level qualifications and jobs.
The rescinding of DACA was announced by Jeff Sessions, Trump's Attorney General.
Sessions said: "We are people of compassion and people of law but there is nothing compassionate about failing to enforce immigration law.
"Failing to do so in the past has put our nation at risk. The compassionate thing to do is enforce the law."
He said DACA had denied jobs to Americans workers because "illegal aliens took those jobs".
Sessions said it had been an "open-ended circumvention of immigration law" and was executive overreach by the previous administration.
Homeland Security Acting Secretary Elaine Duke said the programme would be wound down over six months, which was the "least disruptive option".
It will allow Congress six months to find a legislative compromise to the situation, although Republicans in congress are bitterly divided over the issue.
Duke said no people currently affected by DACA will be affected before March 5 next year. She said: "No new initial requests or associated applications filed after today will be acted on."
