An official investigation into the incident last September has revealed the horn is quieter than the bell, which is routinely used first for warnings.
The UK Department for Transport's rail accident investigation branch (RAIB) found the trams' horn "does not provide a sound pressure level in line with current industry guidance" and "does not generate a greater sound pressure level than the tram bell".
In "urgent safety advice", the RAIB said Edinburgh Trams should "increase the sound pressure level of the warning horn fitted to its trams".
The RAIB said it should also "consider measures to mitigate risks at locations where audible warnings may be required.
"In particular, consideration should be given to the appropriateness of the current warning horn or bell as a method of warning to pedestrians using footpath crossings over off-street track sections with high line speeds."
The advice follows the death of Carlos Palacio, 53, who was hit by a tram around 12:10pm on 11 September while crossing the tracks on a crossing between Balgreen and Saughton tram stops.
Edinburgh Trams said both the bell and the horn were used by the driver when necessary.
It said the bell was used first, but if it did not produce the desired result, the driver could then use the horn.
The horn also comes on automatically if the emergency brake is applied.
The RAIB stated: "The tram driver had observed the pedestrian approaching the crossing and, in response, applied the service brake to reduce the tram’s speed as well as sounding repeated warnings using the tram’s bell.
"The pedestrian did not respond to these audible warnings and continued onto the crossing.
"Although the driver then operated the emergency brake (which automatically activated the warning horn) before arriving at the crossing, the tram was too close to be able to stop before reaching it.
"The tram’s speed at the time of the collision was approximately 50km/h (31mph), and the maximum line speed in this section is 70km/h (43mph)."
The RAIB said following a series of tests, neither the bell nor the warning horn were sufficiently discernible above the level of background noise at the footpath crossing to alert people to the approach of trams.
It also found the warning horn was quieter than the bell because it produced a lower sound pressure level.
The RAIB said when the trams were bought and introduced there were "no specified numeric requirements for the sound pressure levels for tram audible warning devices".
But it said guidance existed that states there should be two levels of audible warnings; the lesser level for on-street use, and the greater for off-street sections and emergencies.
It said: "It is common practice on tramways in the UK that the former is provided by a bell, and the latter by a warning horn."
A spokeswoman for Living Streets, which campaigns for pedestrians, said: "It’s terrible the horn did not follow industry guidance around sound pressure levels, and that a person has died.”
Gavin Booth, director of watchdog Bus Users Scotland, said: "We welcome any action that will make Edinburgh Trams safer for passengers and other pedestrians.
"The warning bell used in built-up areas does appear to be effective and it would be worthwhile if the effectiveness of the horn was improved for other areas where line speeds are greater.
"The large fleet of Metrolink trams in Manchester have a piercing horn that is used in the city centre and certainly acts as an effective audible warning to pedestrians."
A cyclist said: "For too long, cyclists and pedestrians have been at the mercy of trams in Edinburgh."
A spokeswoman for Edinburgh Trams said: "When Edinburgh Trams commenced passenger service in May 2014 we were satisfied that suitable and sufficient testing of the audible warning horn had been undertaken.
"We want to provide a safe tramway for our customers and take cognisance of the notice issued today by the RAIB.
"Further testing is already underway with modifications to the warning horn being implemented across the fleet.
"We continue to work with the RAIB and do not wish to predetermine the outcomes of their final report which is expected in the spring."