The Brazilian was keen to secure a move back to his homeland in order to try to win back his place in the national squad ahead of the 2014 World Cup, but the 31-year-old joined Hoffenheim on Thursday after the Bundesliga side made an approach in the last 24 hours.
The Brazil international joined from PSV in 2008 and went on to become a regular under Harry Redknapp, but a series of high-profile errors saw the former Spurs boss bring in Brad Friedel and Gomes and has struggled to get into the starting XI ever since.
The arrival of Hugo Lloris from Lyon last summer meant Gomes dropped even further down the pecking order. His last appearance for the London club came in November 2011 and he has rarely made the bench in the last 18 months.
Gomes is just one of a number of squad players Tottenham manager Andre Villas-Boas is looking to move on before Thursday night's 11pm deadline.
Andros Townsend may also leave on loan, while young right-back Adam Smith has extended his loan spell at Millwall.