Born in Galați, Neagu began his career with the youth system at Oțelul Galați. He made his professional debut as an 88th-minute substitute in a 1–1 away draw against Brașov on 22 May 2009 and finished 2008–09 season with two appearances. Neagu began to establish himself in the Oțelul first team from the 2009–10 season, making 24 league starts. On 7 March 2010, he scored his first goal in a 1–0 victory over CFR Cluj.
Steaua București
On 3 September 2013, Neagu agreed to join Steaua București after the club agreed a €620k transfer fee with Oțelul Galați.[2]
Cherno More
On 27 June 2019, Neagu signed a contract with Bulgarian side Cherno More Varna.[3]
International career
He has been capped at international level by Romania.