The low-pressure weather system is expected to bring strong winds to Ireland and southern parts of the UK from Friday afternoon to Saturday morning.
The Met Office has moved to issue a yellow warning for winds in southern Wales, as well parts of the south and south-west of England, warning of gusts up to 70mph on coasts.
The warning is due to last from 9pm on Friday until 3pm on Saturday, with forecasters predicting "a risk of disruption to travel".
It is predicted that Hannah - the fourth named storm in the UK and Ireland in 2019 after Erik, Freya and Gareth - will lead to a much cooler Saturday across the country, in contrast to the hot and sunny bank holiday weekend.
Yorkshire will experience increased winds, cooler temperatures and rain shows throughout Saturday as the storm moves across the south of England.
Intermittant rain will begin across the region at 1am with more expected from 10am and again at 7pm.
But a Met Office spokesman said that by the "close of play" on Saturday evening the centre of the low pressure system would have moved on to the Netherlands, meaning the windy and stormy conditions will ease.
After a bright, chilly start cloud will increase from the west.
Showers or longer spells of rain will move eastward throughout the afternoon.
Conditions will turn drier moving into the evening.
Maximum temperature 17 °C.
Weather will continue to be unsettles as Storm Hannah hits the south of the UK.
Showers or longer spells of rain across the region.
Slim chance of thunder.
Increased winds will make it feel chilly and breezy at times.
Sunday is mostly dry with bright or sunny spells returning, especially on the coast.
Winds will die down making conditions feel warmer.