The channel will be replaced with a BBC1 +1 service and many of its shows will be also be shown on BBC1 and BBC2.
In an email to staff, Mr Hall said: "I believe it's the right thing to do: young audiences - the BBC 3 audience - are the most mobile and ready to move to an online world. Twenty-five percent of viewing by 16 to 24 year-olds is to catch-up or other screens and over the next few years we expect that to reach 40%."
Mr Hall said he could not "rule out" further changes to "programmes or services".
The plans, which are subject to approval by the BBC Trust, would save more than £50 million a year, with £30 million of that earmarked to go towards drama on BBC1.
The BBC's director of television, Danny Cohen, a former controller of BBC3, said the move was "the biggest strategic decision the BBC has made in over a decade".
He said: "BBC3 will continue to do all the things we love but it will also have the freedom to break traditional shackles and allow the BBC to be a leader in digital change.
"It will not just be a TV channel distributed online. There is a wonderful creative opportunity here to develop new formats with new programme lengths - and to reach young audiences in an ever-growing number of ways."
Mr Cohen said that "in an ideal world we would not be making this move for a few more years".
He added: "Given an entirely free hand, I would make this change in about four or five years' time, using the years between now and then to slowly shift the balance between linear and on-demand BBC3 content.
"That would be a safer, less risky strategy. But we don't have the choice to wait and do that due to the investments we need to make.
"I want to protect programme budgets from more major cuts across the board and the BBC has to find the money for new obligations including the World Service that will cost £350 million a year."