The Cottagers were impressed with the potential shown by the 16-year-old Danish defender and offered him the chance to join their academy.
However, Gartenmann says he opted to join Dutch side Heerenveen instead as he feels they will offer him a better chance to develop.
The Denmark Under-16 international will officially join the Eredivisie outfit, who are managed by Dutch legend Marco van Basten, on July 1.
"I don't mind the competition for places but I felt that Heerenveen were more interested in developing me as a person as opposed to Fulham where I felt like just another name in the bunch," Gartenmann told BT.
"The fact that the road to first-team football is shorter in Heerenveen had a lot of weight to it and their youth setup is also very competitive. So I'll be training with some of the best young talent on a daily basis."