Spain's Ines Ayala Sender, the EU Parliament's negotiator on the issue, said: "To meet the new EU target of cutting road deaths by half in Europe we need new and more effective road-safety tools to make sure offenders are held to account.
"Everyone in the EU will be treated equally, no matter where their vehicle is registered."
If approved, the bill will apply from May but the UK has two additional years to introduce legislation and for the DVLA to work to update its computer systems.
Brake campaigns officer Ed Morrow said: "For a driver who puts lives at risk to escape prosecution because their vehicle is registered in another country is insulting and incomprehensible for victims. Illegal driving crosses borders, so enforcement must cross borders too."
However, AA president Edmund King said: "In theory, tracking down drivers who break the law in other countries might sound like a good idea in terms of road safety but in practice it could be a nightmare.
"Different European countries have different motoring laws and indeed penalties. Often photographic evidence is not provided. Returning to Europe for a court case is prohibitive in terms of cost."
The Department for Transport said: "It's not right that foreign drivers have gone unpunished for speeding offences in the UK, and we are pleased this is set to change. But it mustn't be easier for British drivers to be prosecuted abroad than for foreign drivers to be prosecuted in the UK."