Scotland, Wales and the north-west of England all had the wettest December in more than a century.
A UK mean temperature of 8C (46F) broke records too and would have felt more like a day in April or May.
The Met Office said storms Desmond, Eva and, most recently, Frank were behind the record rainfall, while a humid south-westerly airflow kept it warm.
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Scotland recorded the most rain in December (333mm or 13 inches), making it wetter than any calendar month since 1910 and far wetter than the average of 204mm (8 inches).
Wales has only seen more rain fall in a single month once than it did in December 2015 - in November 1929.
Central and southern England escaped the worst of it, with rainfall figures much closer to average.
In between the storms, there were warm, sunny days across the UK.
England saw mean temperatures top 9.4C (50F), compared with an average 4.4C (33F) for December.
The Met Office said that, until last week, the year might have looked unremarkable with a cool spring and a cool, damp summer offset by a mild end to the year.
However, this week's rainfall will make 2015 one of the top 10 wettest years since 1910, when the Met Office's digitised records begin. The wettest was 2000, when 1,337mm (53 ins) of rain fell.
Storm Desmond, in early December, brought record-breaking rainfall to the Lake District.
On Christmas Eve, gales and heavy rain from Storm Eva flooded parts of the north-west of England, Scotland and north Wales.
And in recent days, Scotland, Northern Ireland and northern England have borne the brunt of Storm Frank.
Long-standing weather records have been smashed by a stormy, yet warm December, the Met Office's early figures suggest.