A man was shot dead by armed officers at the bridge on Friday afternoon after a number of people were stabbed.
The Metropolitan Police said a device strapped to the individual's body was a "hoax explosive device".
"A male suspect was shot by specialist armed officers from City of London Police and I can confirm that this suspect died at the scene," said Assistant Commissioner for Specialist Operations Neil Basu in a statement.
"A number of other people received injuries during the incident and as soon as we can provide further updates on their condition, we will. Our heartfelt sympathies go out to those anxiously awaiting news from loved ones.
"As you would expect, due to the nature of the incident, we responded as though it was terrorist-related. I am now in a position to confirm that it has been declared a terrorist incident.
Prime Minister Boris Johnson said it was an "appalling" incident.
"I want to thank the emergency services and members of the public for their immense bravery in responding to this suspected terrorist attack at London Bridge," he said.
"This is an appalling incident and all my thoughts are with the victims and their families."
London Mayor Sadiq Khan also thanked the "brave" emergency services and members of the public who risked their own safety to disarm the man.
"They are the best of us," he said, as he asked Londoners "to remain vigilant".
The London Faiths Forum condemned the attack in a statement in which it called on the nation to stand together.
"We, as representatives of many of London's faith communities, deplore the terrible attack that has taken place today at London Bridge," the statement reads.
"All of our religions exalt the sanctity of human life. There is no justification for such a barbaric assault on innocent people. Terrorism has no place on our streets.
"Our prayers are with the victims, their families and all those affected by this terrible act.
"We call for Londoners, and our nation to stand together at this time.
"We will redouble our efforts to work for peace, compassion, understanding and hope. Our message is clear: 'Turn to love.'"
The Church of England has issued a prayer in response to the terrorist attack, which reads:
Lord, ever watchful and faithful,
we look to you to be our defence.
Grant courage to those who protect us,
and comfort to those who are injured and fearful,
as we lift our hearts to know your help,
through Jesus Christ our Lord,