An operation to rescue the drifting platform, carrying construction machinery including a digger, was successfully carried out on Thursday morning.
Boats towed the platform to the industrial port of Hard.
The platform broke free near Chur in the east of Switzerland following days of exceptionally heavy rain.
The 20 Minuten online newspaper quoted a spokeswoman for Graubünden cantonal police as saying the platform belonging to a construction firm was 15 metres long and nine metres wide.
It could not be stopped because of the unusual force of the Rhine. The platform headed north from Chur towards Lake Constance, which Switzerland shares with Germany and Austria.
It reached the mouth of the Rhine on Wednesday evening and ran aground, impeding rescue efforts.
Graubünden police, Swiss and Austrian helicopters and a team from the construction company followed the platform’s progress.
As it was swept along by the fast current the platform hit a number of bridge pillars in Swiss and Austrian waters, shedding some of its load, cantonal police said.
The construction firm has begun disassembling the platform.