The application for Dumfries and Galloway came after recent rain resulted in only a "very small improvement" in stocks at the Black Esk and Penwhirn reservoirs.
Existing services on the Esk Valley line will call at the new stop along with an additional four trains re-routed from Middlesbrough to terminate at Nunthorpe.
Two flood watches are currently in force in Scotland for the east coast from Peterhead to Berwick, and the Solway Firth from the Esk Estuary to Loch Ryan.
The terrace of fishermens' cottages, which are more than 100 years old, overlooks the seaside town from the east side of the River Esk and is just a few hundred yards from the historic Whitby Abbey.
The terrace of fishermens' cottages, which are more than 100 years old, overlook the seaside town from the east side of the River Esk and are just a few hundred yards from the historic Whitby Abbey.