It was discovered a 23m tree at 115 Broadway and a 28m tree at 20 Wicks Street in Bassendean had holes drilled into them and a substance injected into the holes.
While it is unclear when the trees were hit, both had been inspected by staff within the past two months and were healthy.
An investigation by staff has not uncovered the responsible parties.
It will cost the Town of Bassendean more than $8000 to erect the signs and remove the dead trees.
Maintenance on the trees will continue until their removal, including pruning to reduce any public risk issues.
The Town�s move to use signs was inspired by the Swan River Trust, which has used the same method in the past.
After two acacia trees were vandalised in 2012 on Ashfield Parade, the Trust erected a vegetation damage sign in September.
In that case, the trees were cut at the base and the branches were thrown down the embankment.
The sign was removed in March, 2014.
A Trust spokesman said there had been no reports of damaged trees near where the sign had been since it had been removed.
The signs will say: �This tree has been destroyed by a selfish act of vandalism � people found damaging trees will be prosecuted. Please report acts of vandalism to the Town of Bassendean on 9377 8000.�