The 33-year-old arrived at Tottenham in 2008 following a £7.8m transfer from Dutch club PSV Eindhoven.
Gomes made an important contribution in helping Spurs reach the Champions League quarter-finals in 2011.
But the Brazil international made the last of his 135 appearances for the club in November that year.
Gomes has acted as third-choice goalkeeper behind Hugo Lloris and Brad Friedel in recent seasons and made nine Bundesliga appearances on loan at Hoffenheim last season.
A statement from Tottenham read: "Heurelho Gomes is to leave the club at the conclusion of his contract next month and we would like to wish the popular goalkeeper all the best for the future."