The Met Office forecasts that outbreaks of rain, turning heavy at times, will continue until at least 5pm.
It will become breezy later, particularly in areas near the coast.
Ttemperatures will reach highs of 13C.
Outbreaks of rain will gradually ease through the evening as drier conditions move in from the west.
Clearer spells will develop, with winds decreasing.
Temperatures could be as low as 6C overnight and patches of fog are likely in some areas of Yorkshire.
-> Flooding disrupts Northern trains as torrential downpours batter LeedsWhat will the weather be like tomorrow?
Tomorrow is set to be a dry start with fog patches gradually dispersing.
It will be overcast all day, with any brightness limited as increasing cloud eventually brings the chance of rain late in the evening.
Maximum temperatures will hit 13C.
What is the long term weather forecast for Yorkshire?
The Met Office outlook for Tuesday, October 15 to Thursday, October 17 says: "Tuesday, early cloud and rain clearing, then gradually brightening up.
"Wednesday, a dry, bright start but rain and strong winds arriving later.
"Thursday, mostly bright but breezy, with scattered showers."