Data on all passengers leaving the UK is being collected and handed to the Home Office under a scheme being phased in at ports and border crossings.
Transport staff are recording details of all travellers leaving by commercial air, sea and rail transport.
The exit checks were set to particularly affect cross-channel ferry and Channel Tunnel travellers.
The government said they were needed to combat illegal immigration and would cause the "least possible disruption".
Initial reports suggested the new system had started without any major problems, with no delays at the Eurotunnel terminal in Folkestone or P&O Ferries' terminal in Dover.
For the first month all passports will be scanned but only 25% of the passport holders will have their details verified to ensure they are genuine, in a bid to minimise disruption.
After a month, there will be a move to 50% verification and by the middle of June 100% verification will be introduced.
What are exit checks?
Data is being collected on all passengers as they leave the UK on scheduled commercial international air, sea and rail routes.
The government says exit checks are "predominately an immigration and data tool", giving a "comprehensive picture" of whether people leave the UK when they are supposed to.
It says the data - gathered by airline, rail or ferry operator staff - will "improve our ability to identify and further tighten the immigration routes and visas that are most vulnerable to abuse".
It will also help security services "track the movements of known or suspected criminals and terrorists".
School coach parties of European Economic Area children under the age of 16 will be exempt from checks.
Eurotunnel, which manages and operates the Channel Tunnel, said it was moving to 100% checks straight away. It is also asking passengers to provide Advance Passenger Information (API) before travel.
John Keefe, director of public affairs for Eurotunnel UK, told BBC Radio 4's Today programme passengers "shouldn't expect longer queues".
He said some £2.5m had been spent on measures including refurbishing its terminal and that 50 new staff had been recruited.
However, he did call for the introduction of new technology to make the process easier and faster in coming years, saying Eurotunnel expected substantial growth in passenger and truck numbers.
P&O Ferries said a "quiet day" had been chosen for the introduction of the exit checks, with their spokesman adding: "The actual scanning of passports is quick, it's the verification that takes longer."
John Vine, former independent Chief Inspector of Borders and Immigration, told BBC Breakfast: "It will enable the government, for the first time in a long time, to have an idea of who's left in Britain, because up until recently it's not been possible for the government to know who's overstayed their visa and who's remained in the country, and they've not known who's here and who's left."
Immigration minister James Brokenshire said: "Port and travel operators are experts in their business and know their customers best, which is why we've supported them to design and trial the systems for collecting data in a way that will minimise the impact on customers."
The new rules were brought in under the Immigration Act 2014.
The API system, introduced in 2004, already gives the government information on passengers flying in and out of the UK. The exit checks mean information will now be gathered on people leaving by any commercial transport.
People arriving in the UK remain subject to passport checks.