He came through the youth ranks of
FC Groningen, making his debut in the
2007–08 season in a 5–1 lost away match against
NEC, coming in as a second-half substitute for
Koen van de Laak. After playing only seven league matches in two seasons, he signed a loan deal with
Helmond Sport, where his brother
Mark had just signed. Veldmate made his debut for Helmond Sport in a league win (4–0) against
Fortuna Sittard on 7 August 2009. He returned to Groningen after the loan deal, playing only seven matches that season. On 31 May 2011, he signed with
Sparta Rotterdam together with his brother, Mark, for two years. After one season in Rotterdam, Veldmate signed with
Heracles Almelo. Between 2015 and January 2017, Veldmate played in Denmark for
Viborg FF, but his contract was terminated after a series of injuries. In the summer of 2017, Veldmate signed for one year with
FC Emmen. On 2 June 2018, Veldmate signed a two-year contract with
Go Ahead Eagles. On 16 June 2021, he returned to
Emmen on a one-year deal. ==Honours==