Mr Johnson was speaking after returning to 10 Downing Street from a cabinet awayday meeting in Bristol.
He said that ministers were “deeply shocked and heartstricken” to hear of the attack on Sir David, which took place as their special meeting to discuss the upcoming Cop26 climate change summit was beginning.
“I think all our hearts are full of shock and sadness today at the loss of Sir David Amess MP, who was killed in his constituency surgery in a church after almost 40 years of continuous service to the people of Essex and the whole of the United Kingdom,” said the prime minister.
“And the reason I think people are so shocked and saddened is above all, he was one of the kindest, nicest, most gentle people in politics.
“He also had an outstanding record of passing laws to help the most vulnerable, whether the people who are suffering from endometriosis, passing laws to end cruelty to animals, or doing a huge amount to reduce the fuel poverty suffered by people up and down the country.”
Mr Johnson added: “David was a man who believed passionately in this country and in its future. And we’ve lost today a fine public servant and a much-loved friend and colleague.
“Our thoughts are very much today with his wife, his children and his family.”
Mr Johnson’s comments followed tributes from all his living predecessors as prime minister.
Theresa May hailed Amess as “a decent man and respected parliamentarian, killed in his own community while carrying out his public duties” and said his death was “a tragic day for our democracy”.
David Cameron said he was “a kind and thoroughly decent man and the most committed MP you could ever hope to meet”.
Gordon Brown said he was “saddened and shocked” by the MP’s death, while Tony Blair said he was “shocked and horrified” by the killing of “a courteous, decent and thoroughly likeable colleague who was respected across the house”.
Sir John Major said: “This is truly heartbreaking news of a good and decent man who – for over 30 years – was a dedicated public servant. My heart goes out to his family.”
Mr Johnson’s wife Carrie, who shared Sir David’s passion for animal welfare, was one of the first in the political world to respond to his death.
“Absolutely devastating news about Sir David Amess,” she tweeted.
“He was hugely kind and good. An enormous animal lover and a true gent. This is so completely unjust. Thoughts are with his wife and their children.”
Labour leader Sir Keir Starmer said his thoughts were with Sir David’s family.
“This is a dark and shocking day,” said Sir Keir. “The whole country will feel it acutely, perhaps the more so because we have, heartbreakingly, been here before.
“Above all else, today I am thinking of David, of the dedicated public servant that he was and of the depth of positive impact he had for the people he represented.
“Informed by his faith, David had a profound sense of duty that I witnessed firsthand in parliament. His Catholicism was central to his political life and he was highly respected across parliament, within the church and in the Christian community.
“Let us come together in response to these horrendous events. We will show once more that violence, intimidation and threats to our democracy will never prevail over the tireless commitment of public servants simply doing their jobs.”