The warning initially was issued for areas in England but it was extended to reach into Scotland on Tuesday morning as the risk level of the heavy rain forecast increased.
The Met Office has warned residents to expect to see delays to bus and train services, potential flooding of homes and other buildings and spray and flooding on the roads making for difficult driving conditions.
East Lothian and the Scottish Borders are particularly at risk of flooding.
A statement from the Met Office said: “Rain, accompanied with strengthening winds, will continue to affect northeast England and the far southeast of Scotland today before clearing away eastwards this evening.
"A further 15-25 mm of rain is expected quite widely whilst in some places another 40-50 mm is possible.”