He made the announcement in a video messageoutlining what he intends to do first when he takes office in January.
The TPP trade deal was signed by 12 countries which together cover 40% of the world's economy.
Mr Trump also pledged to reduce "job-killing restrictions" on coal production and stop visa abuses.
But there was no mention of repealing Obamacare or building a wall on the southern border with Mexico, two actions he said during the campaign he would do as soon as he assumed power.
His surprise election win two weeks ago has sparked protests across the US.
What is the TPP?
The massive trade deal was agreed in 2015 by nations including the US, Japan, Malaysia, Australia, New Zealand, Canada and Mexico, but is not yet ratified by the individual countries.
Its aim was to deepen economic ties and boost growth, including by reducing tariffs.
There were also measures to enforce labour and environmental standards, copyrights, patents and other legal protections.
But its opponents say it was negotiated in secret and it favoured big corporations.
Why does Donald Trump dislike the TPP?
During the US presidential election campaign, Mr Trump gave broadbrush arguments against the pact, and used plenty of colourful language.
In June 2016 he described it as "another disaster done and pushed by special interests who want to rape our country, just a continuing rape of our country". In another speech he referred to the TPP as "the greatest danger yet".
But while there was plenty of talk about "taking back control" of the US economy, there were few specifics.
Announcing the plan to pull out of the TPP, he said that the US would "negotiate fair, bilateral trade deals that bring jobs and industry back onto American shores".
What has the reaction been to Trump's pledge?
"There is very strong support among the other 11 parties to the TPP to ratify it and to seek to bring it into force. So Mr Trump and his new congress will have to make their own decisions in America's interest." - Malcolm Turnbull, Australian prime minister
"It is Donald Trump's right as the democratically-elected next leader of the United States to make the policy decisions he thinks right." - Najib Razak, Malaysian Prime Minister
"Very depressing news. It means the end of US leadership on trade and the passing of the baton to Asia." - Deborah Elms, Asian Trade Center
"The collapse of the TPP will now create a void in Asia. There is lots of talk about China now moving in to fill it." - Harumi Taguchi, economist
Shortly before Mr Trump released his video, Japanese Prime Minister Shinzo Abe said the TPP would be "meaningless" without the involvement of the US.
Asia-Pacific leaders meeting in Peru over the weekend had said they would continue to pursue free trade deals, despite Mr Trump's opposition.
Analysis: Karishma Vaswani, Asia Business Correspondent
President-elect Trump signalling the death of the TPP is a big blow to many parts of emerging Asia. Sure, the other countries could go ahead, as some have signalled, and continue with the deal on their own - but what would be the point without unfettered access to the US market?
Vietnam and Malaysia were set to gain the most from the deal. They already have access to the US markets for their products, but were hoping to see tariffs on some of their key exports vanish altogether.
China could step in with a regional trade deal, also known as the RCEP. But would a Chinese initiated regional trade deal bring the same benefits? Not really, say some analysts - most Asian countries already have preferential access to China's markets under the China-Asean [Association of South East Asian Nations] free trade agreement of 2010.
But you could see some Asian countries that were due to be excluded from the TPP - like the Philippines, Thailand and South Korea - benefit from the RCEP.
What else did Mr Trump say?
In the video message, Mr Trump said his governing agenda would be based on "putting America first".
The five other executive actions he said he would take on day one are:
- cancelling restrictions on US energy production
- cutting regulations on businesses
- ordering a plan to combat cyber-attacks
- investigating visa abuses that undercut American workers
- imposing a five-year ban on people leaving government to become lobbyists.
What did he say about who would work with him?
The president-elect has spent the last week starting to put together his new team.
He said in the video that "truly great and talented men and women, patriots are being brought in and many will soon be a part of our government".