Born in Bolintin-Vale, Giurgiu County, Matei came through FC Steaua București's youth ranks, and in 2009 he was named the best player of the "Iulian Manzarov – International Football Tournament for Juniors" in Bulgaria. On 16 May 2010 he made his Liga I debut for the senior team, in a 2–0 victory against FC Universitatea Craiova where he came on as a substitute for Romeo Surdu in the 82nd minute; in September, he was sent on loan at fellow league side Unirea Urziceni along with several other teammates from Steaua's reserves. The following year, Matei terminated his contract with the capital-based club. As a result, Steaua owner George Becali criticised the youngster, stating in a controversial manner that he would never become an above average player.
In the autumn of 2013, Matei agreed to a three-year deal with Ukrainian side Volyn Lutsk, having been previously close to joining Dinamo București, the historical rival of his former club Steaua. During his spell with "the Crusaders" he made 61 appearances all competitions comprised, and scored 12 goals.
Rijeka
On 2 February 2016, HNK Rijeka announced they had signed Matei on a three-and-a-half-year contract. He was given the number 10 jersey and made his debut a week later, as an 85th-minute substitute in a 2–0 home win over NK Lokomotiva. He scored his first goal for his new team in the first leg of the Croatian Cup semi-final, helping to a 2–1 defeat of Slaven Belupo. On 9 January 2018, Rijeka loaned Matei to Astra Giurgiu in Romania until the end of the campaign.
Ittihad Kalba
In May 2018, after his loan at Astra Giurgiu expired, he moved to Emirati club Ittihad Kalba for a transfer fee of €500,000. He netted his first goal on 28 September, in a 3–1 victory over Al-Nasr.
Return to FCSB
Matei returned to his boyhood club Steaua București—now renamed FCSB—on 4 January 2019, seven years after stating that he did not regret leaving the Roș-albaștrii and being subsequently criticised by owner Gigi Becali.
Return to Astra Giurgiu
On 19 June 2019 he signed a 1-year contract with Liga I side Astra Giurgiu.
International career
Matei earned caps for Romania's under-17 and under-19 teams. In early 2016, Romanian coach Mircea Lucescu regarded him as a player who would deserve to be selected for the full side.
