The team, captained by Colin Montgomerie, clinched victory at Celtic Manor in South Wales on Monday.
The tournament had run into a fourth day for the first time in its history as a result of bad weather.
The PM said:
Congratulations to Colin Montgomerie and the Europe team on a stunning Ryder Cup victory.
After a stormy weekend, we will long remember the drama of the first ever Ryder Cup Monday played in the Welsh sunshine.
Well done also to the crowd at Celtic Manor who more than played their part.