Provisional figures show the UK had an average 132.9mm of rainfall.
The all-time record for March is 150.3mm, which was set in 1981.
The amount of rain varied across the country.
Scotland as a whole recorded its fifth wettest March, Wales its seventh and England its 16th.
But by 18 March enough rain had fallen to make it the wettest March on record in Northern Ireland.
North-west England and north Wales saw their second wettest March.
Two named storms, Storm Freya and Storm Gareth, passed over the UK during the month, bringing heavy rain, strong winds and snow to many parts of the country.
Provisional figures also show the average mean temperature across the UK was 6.8C – high enough to rank as the 10th warmest March on record.
There was an average 115.6 hours of sunshine, which was some way below the record of 169.5 hours set in 1929, but slightly above usual for the time of year.
Met Office temperature and rainfall data goes back to 1910, while sunshine data begins in 1929.