The son of professional basketball players, Veremeenko was an early bloomer as he started his career with local side
Gomel aged 15, playing in the
1999–00 Korać Cup before making the
Belarusian league All-Star Game the next season. He moved to Russian club
Avtodor Saratov in 2002, averaging 14.2 points and 7 rebounds per game during his second season in the
Russian Super League. When club owner Vladimir Radionov moved the club to Saint Petersburg to form
Dynamo, Veremeenko followed him. He would contribute 12.6 points and 5.5 rebounds per game to the club's
2005 FIBA Europe League title. He did not join the club, moving to another Super League side,
BC Khimki, later that year following Dynamo Saint Petersburg's bankruptcy. Spending two seasons with the club, Veremeenko did not manage to crack the first team and found himself frustrated by his substitute status, even as the Russian team fought for titles (winning the 2008
Russian Cup). with his rights used as a makeweight in a 2010 salary-cap motivated deal which brought
Kirk Hinrich and
Kevin Séraphin from the
Chicago Bulls. On July 7, 2016, his rights were traded to the
Cleveland Cavaliers alongside
Mike Dunleavy Jr. for the draft rights of
Albert Miralles, which was done in order for the Bulls to sign
Dwyane Wade. On August 7, 2018, his rights were traded to the
Los Angeles Clippers for
Sam Dekker, rights to
Renaldas Seibutis and cash, with Clippers aiming to free up a roster spot. Signed by
UNICS Kazan in August 2008, the big man quickly rediscovered his form. and the
2011 EuroCup. He moved to Spanish side
CAI Zaragoza in August 2014, but bought out his contract a month later to accept a better paid offer from Turkish outfit
Banvit, not even playing a friendly game with the Spaniards. His time with Banvit would see him break the all-time
EuroCup record for total rebounds with a new mark of 476 over eight seasons, ending the season with 543; from averages of 9.1 points and 4.3 rebounds per game in the competition in addition to 10.4 points and 5.1 rebounds in the
Turkish Super League. On 18 August 2015, Veremeenko signed with Italian
Serie A outfit
Grissin Bon Reggio Emilia for one year. On September 2, 2019, he has signed with
Tsmoki-Minsk of the
VTB United League. ==International career==