Minev, together with his twin brother, started his career at
Hebar Pazardzhik. Later, Minev joined
Botev Plovdiv.
Levski Sofia Minev came to Levski in June 2006. On 9 May 2009, Minev and his twin brother
Yordan entered in the history of
The Eternal Derby. The situation was even more interesting, because Veselin was a left full-back and his brother Yordan was a right midfielder, and Veselin guarded his brother Yordan. Despite the tackles, after a foul against Veselin, Yordan came to him and call the referee. He became a
Champion of Bulgaria in 2008–09 season. In 2009–10 season, Levski achieved qualifying for
UEFA Europa League becoming third in the final ranking. During the 2010–11 Levski qualified for
UEFA Europa League after eliminating
Dundalk F.C.,
Kalmar FF and
AIK Fotboll. Levski was drawn in
Group C, facing
Gent,
Lille and
Sporting CP.
Antalyaspor in 2011 On 30 May 2011, Minev signed a three-year deal with Turkish club
Antalyaspor for an undisclosed fee. He left the club in early December 2012 for personal reasons.
Botev Plovdiv On 12 December 2012, immediately following the appointment of
Stanimir Stoilov as head coach, Minev signed a 1.5-year contract (with the option for an additional year) with his former club
Botev Plovdiv. Minev was among the first choice defenders during his time with the "canaries",
captaining the team on occasions. His last game for the club was a 4–0 home victory against
Libertas in the first qualifying round for UEFA Europa League on 3 July 2014.
Levski Sofia In July 2014 Minev's contract with Botev was terminated due to the financial problems that occurred in the club. On 7 July 2014, he returned to Levski signing a new 1+1 year deal with the club. He was released in June 2017.
Etar On 16 June 2017, Minev signed a one-year contract with newly promoted
Etar Veliko Tarnovo.
Vereya On 13 January 2018 Minev joined
Vereya Stara Zagora on a six-month contract.
Tsarsko Selo On 11 June 2018, Minev signed a one-year contract with
Second League club
Tsarsko Selo. ==International career==