In October 2018, Andreev reached the semifinals in singles at the 2018 Summer Youth Olympics and the final in doubles winning the silver, teaming with Australia's Rinky Hijikata.

Andreev made his debut at ATP level at the age of 15, when he received a wildcard for the qualifications of the 2016 Moselle Open, where he lost to Michael Berrer.

Andreev played as a wildcard at the 2017 Sofia Open in his homeland for the first time, losing in two sets to Maximilian Marterer in the qualifications.

The following year, Andreev received another wildcard, this time for the main draw of the 2018 Sofia Open event,[6] but lost to Denis Istomin.

[9] At the beginning of the season, Andreev qualified for the main draw of the Antalya Open and managed to record his first ATP win defeating Marsel İlhan in straight sets before he lost to the eventual champion Alex de Minaur in the second round.

[10] In January, Andreev reached his first Challenger semifinal as a qualifier at the 2022 Città di Forlì II where he lost to third seed Jay Clarke.

In April, he also reached the quarterfinals at the 2022 Sarasota Open[11] but retired against fifth seed and eventual champion Daniel Elahi Galán.

In August, Andreev reached his first Challenger final in doubles at the IBG Prague Open, playing alongside Murkel Dellien, but the Bulgarian-Bolivian duo lost in the title match to Victor Vlad Cornea and Andrew Paulson.

[14] The Bulgarian's third Challenger quarterfinal showing came at the Open de Rennes tournament in September, where in the round of 16 Andreev scored his second Top 100 win, overcoming the world No.

309 at the AON Open Challenger in Genoa, he entered the main draw as an alternate and started his campaign with a win over former top-100 player Salvatore Caruso.

64 and third seed Corentin Moutet, saving three match points for his third Top 100 win of his career to reach his fourth quarterfinal of the season.

With his next straight sets win over Raúl Brancaccio, he reached his second Challenger semifinal and the top 250, climbing more than 60 positions in the rankings.

The next day he further reached the top 200 with a round of 16 showing at the Challenger 2022 Copa Faulcombridge in Valencia with a win over sixth seed Timofey Skatov.

He made his 2023 United Cup debut in the mixed doubles match alongside Gergana Topalova where they lost to the top seeded team of Maria Sakkari and Stefanos Tsitsipas.

At the 2024 Zadar Open, Andreev reached his maiden Challenger final defeating Manuel Guinard, wildcard Matej Dodig, Enrico Dalla Valle and Timofey Skatov.

[30] In August, Andreev won his maiden Challenger title in Porto, defeating fourth seed Carlos Taberner in the final.