Disclaimer: The following is derived from my understanding of US policy (it should be noted that I am from Canada so my understanding of US policy is limited to a few branches of environmental government). Additionally, my degree is in Earth and Environmental Science. While there is some overlap in ecology, specifically in relation relation to species trends which are related to the spatial properties of landscapes, I am by no means an expert.
It's firstly important to consider the actual definitions of what an "invasive species" is, and where those definitions are sourced.
That provided by the USDA, whose function is in agriculture, is two-fold. The species must be from somewhere else, and that species must be detrimental to factors that the USDA governs (i.e. cause economic or environmental harm, which could potentially affect agriculture output).
Alternatively, the US Environmental Protection Agency (EPA) defines an invasive species as follows:
"A type of plant, animal, or other organism that does not naturally live in a certain area but has been introduced there, often by people. An invasive species can spread quickly, especially if it has no natural predators in its new home. An invasive species can hurt native species, disrupt ecosystems, and create problems for people (for example, weeds and insects that damage crops)."
In this case the only essential trait which defines the a species as 'invasive' is the fact that it is non-native, though there may be addition consequences (which are often more likely than one would think).
Fundamentally each definition is correct, it depends on the intent of usage.
Given that I am not a stakeholder in agriculture and am in the environmental sector, I am more likely to consider the later definition, considering that Chameleons ARE an invasive species in Florida.
That being said, I do not consider them a threat to current ecosystems. They are arboreal and tend to be opportunistic insectivores (so bugs [which there are a heck of a lot of] that get too close tend to be eaten). As much as we joke, chameleons are quite slow. Small animals that live in trees tend to have a very small range of movement in their lifespan, which greatly impedes the spatial progression of a species through time. At this point chameleons do not seem to impact ecosystems, though nothing is certain and if populations continue to increase through anthropogenic release there could be change (which is hard to predict, given the complexity and sensitivity of ecosystems, complexed by lags in time between environmental stress and environmental response).
Punchline: I would consider chameleons invasive, though currently non-threatning!
!!! Also, the most humane way is to let them live a long and happy life in my backyard 
(too cold here though 
). Nuisance still wouldn't be invasive in my opinion for what its worth 
. 
