The 19-year-old Swiss centre-half, who signed for the Blues from Lausanne in 2008, scored a rare goal on what turned out to be his farewell appearance in a 3-1 EDS win at Bury last week.
Veseli skippered Switzerland to victory in the FIFA Under-17 World Cup in Nigeria in October 2009, where his team beat the host nation 1-0 in the final.
He made his EDS debut off the bench against Wigan in April 2010, and made his senior debut in a 2-0 win over Club America in San Francisco on the tour of North America last summer.
But despite being on the bench for the Carling Cup tie at West Brom last season, Veseli, who can also play as a holding midfielder, has found it difficult to progress further.
He leaves with the Club’s best wishes for the future.