The recommendation was made by the House of Lords EU Committee, which has been looking into what rules are needed to safeguard the use of unmanned aircraft.
It suggests the database would initially include businesses and other professional users, and then later expand to encompass consumers.
However, one expert questioned how useful such a register would be.
The committee's report warned that over-regulation risked stifling the drone industry, estimating that it could be responsible for creating as many as 150,000 jobs across Europe by 2050.
Even so, it suggested that creating the database would help the authorities manage and keep track of drone traffic.Growing numbers of drones can be bought over the internet and flown without a special licence
In addition, it made several other recommendations, including:Greater use of geo-fencing - programming drones not to be able to take off from or fly into certain locations based on their GPS co-ordinates. This could include airports, prisons and other high risk sites Clearer guidance for police about how they should enforce existing safety rules The use of a kite mark or other logo to denote drones that have been classed as safe to use More guidance to be given to commercial drone operators about what insurance cover they need to buy
"We have a huge opportunity to make Europe a world leader in drone technology," said committee chairwoman Baroness O'Cathain.
"But there's also a risk. It would just take one disastrous accident to destroy public confidence and set the whole industry back.
"So, we need to find ways to manage and keep track of drone traffic.
"That is why a key recommendation is that drone flights must be traceable, effectively through an online database, which the general public could access via an app."Amazon says it intends to make deliveries by drones if it can get regulatory approval 'Limited awareness'
The UK's current regulations are set by the Civil Aviation Authority (CAA).
It prohibits unmanned aircraft from flying closer than 150m (492ft) to any congested area, or within 50m (164ft) of any vessel, vehicle or structure that is not in the control of the person in charge of the aircraft.
The CAA typically bans the use of drones weighing over 20kg (44lb), but lower than that weight they can be used if they remain in the operator's line of sight.The Lords suggest that the media will increasingly use drones to take photographs and video if regulations do not stifle the activity
A report by the University of Birmingham last year noted that awareness and observance of the regulations was "limited in practice", and added that the UK's Air Traffic Control's system were inadequate to cope with the expected rise in the use of the aircraft.
One of the experts quoted in the report told the BBC he was concerned that the Lords' suggestions did not go far enough.
"Law abiding citizens are likely to register, but it would be very difficult to stop terrorists and other criminals from purchasing drones abroad and then using them here," said Prof David Dunn, who has written about the matter for The Royal Institute of International Affairs.
"The technologies have the capacity to crash into people and kill them, as they have done in the States, or indeed they can potentially be used to fly into the engines of jets creating a mechanical bird-strike effect. Some of them can be used to carry 1kg [2.2lb] of weight - so they could be used to carry explosives or indeed to spray vapour.
"Up until now it was expensive and required skill to be able to fly an aircraft - which acted as a form a regulation in itself. Now, you can fly these things relatively easily over people's heads.
"I'm not sure this has been thought through as much as it might have been."Experts warn that drone owners often have "limited" knowledge of rules governing their use Testing our tolerance
By contrast, the committee highlights drones' potential for good - carrying out "dull, dirty or dangerous jobs" including goods deliveries, search-and-rescue operations and geographic surveys.
The Economist newspaper has also pointed out that drones can be used to improve - rather than threaten - public safety, by making it relatively cheap to inspect wind turbines for cracks and carry out power-line inspections.
However, one expert from Imperial College noted that if the EU's use of drones rose as quickly as the Lords suggested, then the public's tolerance for related accidents would likely be put to the test.
"It's the scale of the accidents that I'm worried about," explained Dr Ravi Vaidyanathan.
"If a drone flying at relatively low speed scratches the side of my car and I have to get it fixed, but the drone's owner or manufacturer's insurance covers the costs, then I think there is a high tolerance for things like that.
"But if, for example, a drone cuts someone or hits the windshield of a car forcing it off the road, then I don't think the public is going to accept that."