The 27-year-old has spent five seasons at the Dragons and during that time led Wales to Grand Slam glory in 2005.
"I was very excited about the future for Saracens and I wanted to be part of it," he said.
Owen's decision to quit Wales comes a week after Scarlets scrum-half Dwayne Peel agreed to join Sale Sharks next season.
The two deals seem to ignore Wales coach Warren Gatland's warning that players may jeopardise their international careers if they play outside Wales.
But the WRU insists the new policy is mainly aimed at the next generation of Wales players, and does not apply to current squad members with non-Welsh clubs.
Owen is not included in the Wales squad for this season's RBS 6 Nations championship, but he hopes the move to Saracens will help him get back into the squad and add to his 41 caps.
"I am really looking forward to the fresh challenge and the chance to compete in the Guinness Premiership and in Europe," he said.
"I've also still got strong international ambitions for Wales, and I am sure that being part of the success at Saracens will help with that.
"It is a big decision to leave the Dragons and move my family, but it is one which feels right."
Saracens director of rugby Alan Gaffney said: "Michael is a very hard-working player who has high skill levels, and he will fit in well with the style we want to play at the club.
"He is also in the prime of his career, and his arrival next season will really strengthen the squad."