Bachmann has spent the past several months on the Spanish island after his family could no longer take the pressure of living in Dresden, where Pegida is based, according to the Sächsische Zeitung (SZ).
In a video published on Facebook, Bachmann claimed he and his wife were being “persecuted”, citing several attempts to break into his home.
But he did not confirm that he was now living permanently on the island off the west African coast. He had been on the island for the past four or five months following employment opportunities, he claimed.
Pegida - full name the Patriotic Movement against the Islamisation of the Occident - emerged in November 2014 as a street movement against immigration from Muslim countries. At its high point it drew tens of thousands of people onto the streets of Dresden and has since created offshoots in many other German cities.
The 43-year-old Bachmann is the head of the movement, but the irony of him being able to escape visa-free to a colonial remnant of the continent where so many refugees come from has no doubt been lost on him.
As well as being photographed sporting a Hitler-style hairstyle and moustache, he has also been found guilty of inciting hatred after he referred to refugees as “scum” and “cattle” in a series of Facebook posts.
But, whereas Bachmann was once ever present at the weekly Monday evening Pegida marches in Dresden, in recent months he has been notable for his absence, the SZ reports.
That he has flown off to Tenerife was revealed on Facebook by Tatjana Festerling, once co-leader of the organization, but who after conflict with Bachmann was turfed out of the leadership.
In the Facebook post, Festerling claimed that Bachmann only comes back to Germany every two weeks for “a show of resistance.”