The apps will be barred from requiring passengers to disclose their destinations when they make bookings due to concerns some taxi drivers may try to avoid certain routes, the LTA said.
Operators are also required to provide "basic customer support", including lost and found services and a platform for customers to file complaints.
Passengers in Singapore can only use Uber to connect to registered taxis and limousines, unlike in some other cities around the world where the app is used to hire private cars and ride-share to cut fares.
Other similar apps operating in Singapore include Britain's Hailo, regional player Easy Taxi and Malaysia-based GrabTaxi.
At present, these apps already comply with Singapore's new requirement for the taxis to be licensed.
Michael Brown, Uber's Southeast Asia general manager based in Singapore, on Friday welcomed the new rules.
"We appreciate that the LTA has acknowledged the benefits our technology brings, and like Uber, is putting the interest and safety of consumers and drivers first," Brown said in a statement to AFP.