The Glasgow climate deal is a "game-changing agreement" which sounds "the death knell for coal power", Boris Johnson says.
Although countries only agreed to "phase down" rather than "phase out" coal, the prime minister said this was a fantastic achievement.
The wording change was made after a late intervention by China and India.
But it remains the first time plans to reduce coal have been mentioned in such a climate deal.
The agreement was reached after the two-week Glasgow COP26 summit went into overtime on Saturday.
Critics have said the deal does not go far enough and will not meet the key summit goal of limiting global warming to 1.5C by the end of the century.
Scientists say this would limit the worst impacts of climate change.
During a Downing Street news conference, Mr Johnson said:
- "We can lobby, we can cajole, we can encourage, but we cannot force sovereign nations to do what they do not wish to do"
- "For all our disagreements, the world is undeniably heading in the right direction"
- The "tipping point has been reached in people's attitudes" - with leaders "galvanised and propelled by their electorates"
- But "the fatal mistake now would be to think that we in any way cracked this thing"
Mr Johnson said that despite the achievements of the summit, his reaction was "tinged with disappointment".
He said there had been a high level of ambition - especially from countries where climate change was already "a matter of life and death".
And "while many of us were willing to go there, that wasn't true of everybody", he admitted.
But he added the UK could not compel nations to act. "It's ultimately their decision to make and they must stand by it."
Mr Johnson also said he thought the watered-down language on coal did not "make that much of a difference", adding that the direction of travel was "pretty much the same".
He said most of Western Europe and North America had been persuaded to pull the plug on financial support for overseas fossil fuel projects by this time next year.
"And when you add all that together, it is beyond question, Glasgow has sounded the death knell for coal power," he said.
Speaking alongside the PM, COP26 president Alok Sharma revealed that at one point during the final negotiations, he had feared the agreement was in jeopardy.
"There was an hour where really we weren't going to get a deal," he said.
Mr Sharma, who fought back tears as he closed the summit following the late intervention, said: "I can tell you there was one really tense hour where I did feel the weight of the world on my shoulders... this deal was absolutely in jeopardy. We got it over the line."
Earlier he said that "China and India will have to explain themselves" to climate-vulnerable nations.
One of the main goals set out by COP26 was to ensure global warming does not go above 1.5C by 2100 - but a report by the Climate Action Tracker group has calculated that at the current rate, the world is heading for 2.4C warming by that date.
As part of the agreement struck in Glasgow, countries will meet next year to pledge further major carbon cuts with the aim of reaching the 1.5C goal.
Under the Glasgow climate pact:
- Countries were asked to republish their climate action plans by the end of next year, with more ambitious emissions reduction targets for 2030
- There is an emphasis on the need for developed countries to increase the money they give to those already suffering the effects of climate change - beyond the current $100bn annual target
- The language about coal has been included for the first time ever in a global climate deal
- A pledge in a previous draft to "phase out" coal was instead watered down to a commitment to "phase down" coal
The UN's climate change chief Patricia Espinosa described the mention of fossil fuels as a "huge step forward" but added there was a need to "balance out the social consequences" for people of cutting coal power - particularly in poor countries.
She said that the 1.5C target was "definitely alive" but, earlier, Labour's shadow business and energy secretary Ed Miliband said the goal was "in intensive care".
Climate stripes visualisation courtesy of Prof Ed Hawkins and University of Reading.