The two-day yellow warning has been issued by the Met Office for Tuesday and Wednesday and gusts could reach speeds of 40mph.
Forecasters warn strong winds and gales are likely to bring travel disruption.
Drivers of high-sided vehicles should avoid exposed routes and bridges.
Buses and trains could also be affected, with journeys from Leeds likely to take longer than usual.
Unplanned power cuts are also possible.
What is the weather forecast for Leeds?
Tuesday is set to be a washout with heavy rain forecast throughout the day. Strong winds will pick up reaching up to 40mph on Tuesday night. Temperatures around 19C.
The rain will clear on Wednesday however the yellow warning for wind is still in place. Forecasters expect winds to ease by Wednesday evening, but further rain is possible on Thursday.
Heavy rain forecast for Leeds
Heavy rain during Tuesday and early Wednesday and is expected to result in some flooding and disruption to travel.
What to expect
Bus and train services probably affected with journey times taking longer
Spray and flooding on roads probably making journey times longer
Some interruption to power supplies and other services likely
Flooding of a few homes and businesses is likely
Strong wind forecast for Leeds
Storm Francis will bring some very strong winds leading to disruption to travel and power supplies along with potential damage to trees.
What to expect
Injuries and danger to life from flying debris are possible
Some damage to buildings, such as tiles blown from roofs, could happen
Road, rail, air and ferry services may be affected, with longer journey times and cancellations possible
Some roads and bridges may close
Power cuts may occur, with the potential to affect other services, such as mobile phone coverage
Injuries and danger to life could occur from large waves and beach material being thrown onto sea fronts, coastal roads and properties
How to stay safe in a storm
Before the storm
Secure loose objects such as ladders, garden furniture or anything else that could be blown into windows and other glazing and break them
Close and securely fasten doors and windows, particularly those on the windward side of the house, and especially large doors such as those on garages
Park vehicles in a garage, if available; otherwise keep them clear of buildings, trees, walls and fences
Close and secure loft trapdoors with bolts, particularly if roof pitch is less than 30°
If the house is fitted with storm shutters over the windows then ensure that these are closed and fastened
If chimney stacks are tall and in poor condition, move beds away from areas directly below them
During the storm
Stay indoors as much as possible
If you do go out, try not to walk or shelter close to buildings and trees
Keep away from the sheltered side of boundary walls and fences - if these structures fail, they will collapse on this side
Do not go outside to repair damage while the storm is in progress
If possible, enter and leave your house through doors in the sheltered side, closing them behind you
Open internal doors only as needed, and close them behind you
Take care when driving on exposed routes such as bridges, or high open roads, delay your journey or find alternative routes if possible
Slow down and be aware of side winds, particular care should be taken if you are towing or are a high sided vehicle
Do not drive unless your journey is really necessary
After the storm
Be careful not to touch any electrical/telephone cables that have been blown down or are still hanging
Do not walk too close to walls, buildings and trees as they could have been weakened
Make sure that any vulnerable neighbours or relatives are safe and help them make arrangements for any repairs