The warning, which applies to south-west Scotland until 18:00, includes the area west of Dumfries as well as Stranraer. There is the possibility that homes could be flooded, while bus and train services are likely to be affected with travel times taking longer.
Spraying and flooding on roads can also mean that journeys can take longer.
Met Office meteorologist Alex Deakin said rain would rise earlier in Scotland and Northern Ireland on Tuesday, leading to turbulent and wet conditions.
In contrast, Eastern England will enjoy largely “pleasant” and dry weather with the possibility that temperatures will reach peaks of 24C.
He said: “Here comes the next weather system, though it turns into a pretty wet night for Northern Ireland.
“And that rain is really starting to show up and at dawn over southwestern parts of Scotland.
“Elsewhere, that largely clear sky will allow temperatures to drop to single digits through central and eastern parts of England, certainly in rural areas.
“But a nice sunny start here on Tuesday. And actually it’s going to be a pretty pleasant summer day for a large part of East England.
“But further west, a wet start for Northern Ireland and a wet old day for western parts of Scotland.
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“Much of Eastern Scotland, Northern Scotland looks dry.
“A lot of East England also with sunny times that feel quite pleasant 20 to 23, possibly even 24C.
“But stormy and increasingly wet conditions on this west coast mean it will feel quite cool for the time of year.
“The weather front will continue to work eastwards until Tuesday evening.
“Tend to break up a bit as it goes so the rain will not be so persistent.
“But it still looks pretty wet through the night over much of northern England and the Midlands.”