Working together, we can secure a just and prosperous world for all.
Workers are being urged to support school climate change strikes later this month by taking 30 minutes of action.
The TUC Congress voted to call for "workday campaign action" to coincide with the global action on September 20.
Unite assistant general secretary Steve Turner told the conference in Brighton: "As trade unionists we're at the centre of the debate on just transitioning energy generation, our auto industry from the combustion engine to hybrid, full battery and hydrogen, and our ceramics, steel and construction industries from heavy pollutants to sustainable long-term low-carbon producers.
"How proud can we be of our children, knowing it's their future at stake, taking to the streets, just as they did in 2010 in the fight against austerity, to demand the urgent action that is desperately needed.
"As trade unionists, as socialists seeking that better, fairer world, it's our duty to stand proudly alongside them in this fight.
"If we don't, we'll be seen as irrelevant - not as allies in their fight and not an integral part of their future."
University and College Union general secretary Jo Grady said: "The trade union movement is sending a clear message today that it is up to the challenge of fighting the climate crisis and building a stronger and greener economy.
"Climate change is a trade union issue and our planet's future is at risk. The work done by Greta Thunberg and school students around the world has been inspirational and now it's time for the rest of us to catch up."
Jake Woodier from the UK Student Climate Network said: "We're delighted to see the trade union movement making big strides forward in its response to the climate crisis.
"We're calling for ambitious and bold solutions to the crisis like a Green New Deal to create millions of well-paid, secure and unionised jobs, massive investment in marginalised communities and a just transition for those in today's high emissions sectors.
"Working together, we can secure a just and prosperous world for all."
Alan Jones is a reporter with PA.