Mr Yousaf was speaking at New York Climate Week where he called on governments to accelerate financial support for countries most affected by climate-induced loss and damage.
The Scottish Government has led the way on loss and damage, pledging £7 million in climate reparations and helping the issue be put on the agenda at COP27 last year.
The FM said that £5 million has been awarded to the climate justice resilience fund which supports vulnerable communities in the Global South on the front line of the climate crisis.
He also confirmed the Scottish Catholic International Aid Fund (SCIAF) will receive a further £300,000 to support communities in Malawi impacted by Storm Freddy.
Scotland’s Humanitarian Emergency Fund will also receive an additional £1 million to support communities affected by disasters, disease or conflict.
Last month, The Herald exclusively revealed that the additional £5 million pledged by Nicola Sturgeon at COP27 for loss and damage had not been allocated to any projects.
But in his speech in New York, Mr Yousaf said the entire £7 million “has been allocated in full” and is no longer “sitting in the government’s treasury”.
He added: “We are putting our money where our mouth is and ensuring the people who need it the most receive it.”
The First Minister also announced that the Climate Justice Resilience Fund – to which the Government has pledged £36 million by the end of this Parliament – would be delivering a programme aimed at tackling the non-economic impacts of climate change, such as gender-based violence and health impacts, using £5 million of Scottish Government funding.
Mr Yousaf said that leaders of Western nations “are collectively guilty of catastrophic negligence”, adding that “our children have every right to be angry and they have every right frankly not to forgive us if we do not step up”.
He said: “Not a single community on earth will be left untouched by the effects of climate change, but that suffering is not divided equally.
“It is for this reason that our acts of global solidarity as a community are more important now than ever before.”
The First Minister stressed that is was “our moral obligation” to ensure funds reach where they are needed, adding that “pledging is the easy bit”.
He added: “At a time when budgets are tight, believe me I know, it is hard for governments and businesses to do this.
“But funding must not only be pledged, it must be mobilised.
“Pledges alone don’t rebuild communities, pledges alone don’t fund flood resilience, pledges alone don’t fund a just transition.
“It is money – not pledged but deployed – that makes the difference. It is action and help on the ground that makes the difference.”
He stressed that “Scotland can play a significant role in calling for greater international action”.
The First Minister called on politicians and leaders to “rededicate ourselves to the cause of climate justice”.
He said: “Let us pledge not to offer mere warm words, but action.
“I can pledge Scotland will continue to play our part.”
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Mr Yousaf added: “We will transition from being the oil and gas capital of Europe to unleashing our renewable potential and becoming the net zero capital of the world.
“We will show moral leadership and ensure funding for loss and damage is not just pledged – but paid, and I would urge other nations to join us.
“The very existence of our planet and humanity depends on it.”
A leading charity has praised Mr Yousaf’s commitments to the Global South, but warned it needs to be backed up with more climate action in Scotland.
Lewis Ryder-Jones, Oxfam Scotland’s policy adviser, said: “The Scottish Government should be commended for the pioneering role it has played in setting aside dedicated climate justice funding to support low-income countries, in particular, to address the losses and damage they’ve faced.
“More countries must follow Scotland’s lead by stepping up to the plate and delivering on climate finance.
“However, the Scottish Government’s recurrent failure to both meet its own emission reduction targets and to unequivocally oppose new oil and gas, risks making the First Minister’s international climate efforts akin to repeatedly throwing a brick through someone’s window while offering to pay for the damage.
“The Scottish Government needs to urgently scale up its domestic climate action, but that action will be costly. Who foots the bill is a test of political courage and will.
“The First Minister must demonstrate the same leadership he’s shown on climate finance by maximising the use of devolved tax powers while also pressing the UK Government to use all of the levers at its disposal to fairly tax the biggest and richest polluters who’ve done the most to cause the climate emergency.”