The yellow warning, which runs until 9am, covers Dumfries, Galloway, Lothian and Borders.
There is a possibility of flooding in those areas, while transport could also be affected.
The Met Office says: “Thundery showers are likely to become slow-moving over parts of northern England and southern Scotland this evening, perhaps merging into longer periods of thundery rain during Sunday night and Monday morning.
“Heavy downpours could see a few spots receive 20 to 30mm of rain in an hour, or 40 to 50mm in several hours. Many places within the warning area will miss the heavier rain, however.”