The draft law, which aims to ensure "deforestation-free supply chains" for the 27-nation EU, was hailed by environmental groups as "groundbreaking".
It requires companies importing into the EU to guarantee products are not produced on land that suffered deforestation after December 31, 2020, and that they comply with all laws of the source country.
The scope encompasses palm oil, cattle, soy, coffee, cocoa, timber and rubber as well as derived products such as beef, furniture and chocolate.
The European Union is the second-biggest market for consumption of the targeted products after China.
Pascal Canfin, chairman of the European Parliament's environment committee, hailed the agreement, and how its impact would feed through to everyday items Europeans consume.
"It's the coffee we have for breakfast, the chocolate we eat, the coal in our barbecues, the paper in our books. This is radical," he said.
The United Nations' Food and Agriculture Organization estimates that an aggregate area of land bigger than the European Union, or some 420 million hectares (more than one billion acres), has been deforested around the world over the past three decades.
Both the European Council -- representing the EU countries -- and the European Parliament now have to officially adopt the agreed law. Big companies would have 18 months to comply, while smaller ones would get a longer grace period.
The parliament said in a statement that the law opened the way for technology such as satellite monitoring and DNA analysis to verify the provenance of targeted imports.
High-risk exporting countries would have nine percent of products sent to the EU checked, while lower-risk ones would have lower proportions scrutinized.
Companies found violating the law could be fined up to four percent of annual turnover in the EU.
The legislation would be reviewed one year after coming into force, to see whether it should be extended to other wooded land.
Another review at the two-year mark would have the commission considering whether to expand it to cover other ecosystems and commodities, as well as financial institutions.
"The new law will ensure that a set of key goods placed on the (European Union) market will no longer contribute to deforestation and forest degradation in the EU and elsewhere in the world," the European Commission said in a statement.
"The battle for climate and biodiversity is accelerating," French President Emmanuel Macron tweeted.