Slavchev started his career at home-town club Septemvri Sofia, joining their youth system as a six-year-old.

[7] He made his debut during the 2010–11 season, on 31 October 2010 in a 2–0 home win over Slavia Sofia, coming on as a substitute for Hristo Yanev.

[9] On 19 May 2014, Slavchev signed with Portuguese side Sporting CP on a five-year deal, for a reported fee of 2,5 million euro.

On 17 August 2016, Slavchev joined Polish club Lechia Gdańsk, on a season-long loan, where he would play alongside fellow Bulgarian footballer, Milen Gamakov.

[21] He made his debut on 15 February 2020, in the 0–0 league draw against CSKA Sofia in The Eternal Derby, coming on as an early substitute before being replaced himself towards the end of the match due to injury issues.

[23] On 3 January 2023, despite efforts from Lechia Gdańsk to re-sign him in the winter transfer window,[24] Slavchev joined Polish fourth division side Wieczysta Kraków on a two-and-a-half-year deal, with an extension option.

[25] After playing a marginal role in winning promotion to the third division, Slavchev left the club by mutual consent on 19 June 2024.

[29] On 15 October 2013, in the last match for the qualifications for the 2014 FIFA World Cup against the Czech Republic, he made his debut for the first team as a substitute.