Moller arrives from Malmo in a deal worth around £450,000 after the Sweden U19 international had a medical at London Colney on Monday afternoon.
The striker will join up with Steve Bould's U23 side rather than the first-team and has signed a four-year deal.
Moller spent 18 months in Italy with Bologna before returning to Malmo in January.
The Swede will be joined at the Emirates by Hertha defender Rekik, with the 18-year-old joining in a £1 million deal.
Rekik is highly-rated in Germany and is the younger brother of former Manchester City defender Karim Rekik.