The FC Copenhagen wing-back has agreed personal terms at Maine Road, and signed a three-and-a-half year deal.
The fee for the Danish international could rise to £700,000 depending on appearances.
Jensen has now returned to his native Denmark and will be back to join up with the City squad on Friday before leaving for Watford.
A delighted Jensen said: "They can't promise promotion but everything looks like the club is geared up for it. I'm really pleased."