Spurs made the announcement on the club's official website that they two clubs had agreed a deal and subject to agreeing personal terms, passing a medical examination and obtaining his work permit, Gomes will be a Tottenham player.
The fee is believed to be around £7million and Gomes' arrival is likely to spell the end of Paul Robinson's time at White Hart Lane. The England goalkeeper is thought to be one of the players manager Juande Ramos wants to get rid of.
The 27-year-old will be familiar to Spurs fans as he was part of the PSV team that dumped them out of the Uefa Cup last season.
Gomes was also instrumental in the Dutch club's title success, conceding just 24 goals in 34 Eredivisie league games and has an impressive record at PSV, winning four Dutch championships in his time in Eindhoven.
Gomes becomes Tottenham's third transfer of the summer joining Luka Modric and Giovani Dos Santos at White Hart Lane.