Clermont announced Davies' deal - there is also the option of a third season - on their official website.
The 25-year-old, who has won 37 caps, starred for the British and Irish Lions during their victorious Australia tour earlier this year, playing in all three Tests.
Davies played for Wales in last Saturday's Test match against South Africa, but he suffered a chest injury that forced him off early in the game.
Wales have already confirmed that Davies will miss their remaining autumn appointments with Argentina, Tonga and Australia, while he could also be forced to sit out this season's Six Nations if it is decided that he requires surgery.
He is due to link up with Clermont, last season's Heineken Cup runners-up, next July.
And he becomes the latest Wales international to move into France's Top 14, following the likes of Clermont full-back Lee Byrne, Perpignan's James Hook and Luke Charteris, plus the Racing Metro pair of Jamie Roberts and Dan Lydiate.
Davies' departure from the Welsh regional scene is a huge blow for both the Scarlets and the Welsh Rugby Union, with the regional teams struggling to keep their leading players who are nearing the end of existing contracts.
Clermont sporting director Jean-Marc Lhermet told the club website: "We can only be delighted to welcome Jonathan.
"His profile fits perfectly to the game that we practise.
"Despite his young age, he has a huge experience of high-level matches and is one of the world's best players in his position. He will be an asset to our team.
"Jonathan decided to leave Wales for a new adventure , and we are happy that it is with the 'yellow and blue'.
"In addition to his class, he has determination to help us win new titles in the years to come."
Davies' form on the Lions tour - he started all three Tests as the tourists recorded a first series triumph since 1997 - confirmed his status as one of European rugby's hottest properties.
And a move to France means that one of the Top 14 heavyweights have once again underlined their financial clout.
He will join a star-studded Clermont squad that contains players such as Aurelien Rougerie, Morgan Parra, Sitiveni Sivivatu and Wesley Fofana.
And Davies' departure will put into even sharper focus the futures of several Wales colleagues, with skipper Sam Warburton, full-back Leigh Halfpenny, prop Adam Jones and lock Alun-Wyn Jones among those nearing the end of existing playing contracts.
It is understood that the WRU has earmarked a £1million fund to help the regions keep their prize assets.