It has issued a severe weather warning for 16 of Wales' 22 counties, up to and including Powys and Ceredigion.
The storms are making their way from north west France across the English Channel and south west England.
The warning said: "Although producing a good deal of lightning, amounts of rain are relatively small at present."
The yellow "be aware" warning affects: Bridgend, Caerphilly, Cardiff, Carmarthenshire, Ceredigion, Merthyr Tydfil, Neath Port Talbot, Powys, Rhondda Cynon Taff, Swansea, Vale of Glamorgan, Pembrokeshire, Blaenau Gwent, Newport, Torfaen and Monmouthshire.
It adds that very localised downpours may occur in Wales overnight, before clearing from the south.
It said: "A few places could receive 30 mm of rain within two to three hours, although most places will see much less than this."
The warning is in place from 20:00 BST to 06:00 BST on Friday.
Thunderstorms are expected to move across much of south and west Wales overnight bringing localised heavy downpours, according to the Met Office.