The channel will be replaced with a BBC1 +1 service and an extra hour of children's programmes and some of its existing shows will be shown on BBC1 and BBC2.
Tens of thousands of viewers have signed a petition opposing the move, which has been criticised by unions, but Lord Hall said it was "the right thing to do".
In an email to staff, he said the licence fee had been frozen while the demands on it increased.
He said: "This is the first time in the BBC's history that we are proposing to close a television channel. I can't rule out it being the last change to our programmes or services."
The plans are subject to approval by the BBC Trust. Some £30 million of the savings are earmarked to go towards drama on BBC1.
BBC 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".
Gerry Morrissey, leader of the technicians' union Bectu, expressed concern about the impact on jobs.
"We are disappointed that the BBC has made this decision with very little consideration for its employees."