The thief is currently serving a five year sentence and apparently hoped returning the staff would earn him an early release.
An altar cross was also returned along with the staff. Both items are made of gilded silver and valued at €50,000.
"Their symbolic worth far exceeds the value of the material," said Jochen Reidegeld, deputy vicar of the diocese of Münster, adding that he was "profoundly grateful" to investigators for their work.
Cardinal von Galen (1878-1946) was the bishop of Münster and a revered figure in the church's history. He was beatified in 2005 for denouncing the Nazi's systematic murders of the mentally disabled at personal risk to himself.
The objects are slightly damaged and will need to be restored, said the dome chamber's director Udo Grote.
The two treasures were stolen in 2009 from an exhibition in St Ludger's Basilica in Essen. A gang of thieves hid in the Basilica and waited to be locked in after closing. They were sentenced in February 2011, but the missing treasures were never recovered - until now.