The line from Llandudno Junction and Blaenau Ffestiniog was shut after water reached the platform level at North Llanrwst station.
After the flooding receded, repairs were needed over 100 separate locations, according to Network Rail.
Train services will run to a reduced timetable on Monday.
Network Rail delivery director Francis McGarry said: "The scene that greeted us just after Christmas was incredible.
"Parts of the line were still underwater and where the water had receded it had taken much of the track bed with it."
The Conwy Valley rail route in north Wales has reopened after repairs have been completed following flooding in December.