The 33-year-old goalkeeper spent six years on Spurs' books but fell down the pecking order in recent seasons and made no appearances over the campaign just ended
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However, Gomes was then usurped for the No.1 jersey by Brad Friedel and has since fallen further down the pecking order following the arrival of France international Hugo Lloris.
The 33-year-old spent nine games on loan at Bundesliga club Hoffenheim last season but failed to make any appearances for Tottenham in 2013-14.
"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," read a brief statement on the club's official website.
Gomes made 135 appearances for Spurs and played a key part in the side who reached the quarter-finals of the Champions League in 2010-11.