The former Boro captain, who is due to become a free agent at the end of this month, had previously discussed a possible new deal with officials at the Riverside.
However, he has opted to end his association with the Teessiders after five years and more than 150 senior appearances.
"Emanuel is an experienced player who can also play on the left of the defence," said Hannover coach Mirko Slomka. "He will expand our options in defence greatly."
Confirmation of Pogatetz's departure represents a considerable blow to Boro boss Gordon Strachan, who had been hoping to keep the Austria international on Teesside for at least another season.
Back in January, Pogatetz came close to joining Panathinaikos, only for a proposed £1.5m deal to collapse as a result of a power struggle between competing factions on the Greek club's board.
The defender, who has struggled with a series of knee injuries in recent years, returned to action in the second half of the season, and ended the campaign talking of a desire to sign a new deal with Middlesbrough.
However, Hannover's contract offer is understood to have been significantly more lucrative than Boro's, and Pogatetz will return to the Bundesliga next season after leaving Germany to move to England in 2005.
His exit might not be the only defensive blow Strachan is forced to deal with this month, as Stephen McManus is being primed for a return to his parent club Celtic.
McManus spent the second half of last season on loan at the Riverside, and Strachan is keen to retain his services.
The Scotland international travelled to La Manga with the rest of the Boro squad for a training camp last week, raising hopes of either a permanent switch or a second loan deal next season.
However, sources in Scotland claim Neil Lennon is set to be appointed as Celtic's new permanent manager within the next 48 hours.
Lennon is an avowed admirer of McManus, and is likely to make the defender's return one of his major priorities in the opening weeks of his reign.
** READ MORE MIDDLESBROUGH NEWS IN TOMORROW'S NORTHERN ECHO **