Born in Câmpina, Prahova county, Costescu began playing football with Sterom Câmpina in Divizia D (Romanian Fourth Division), and in 1996 he moved to the representative team of the same town, Poiana Câmpina, in Divizia B, the Romanian Second Division. He played 2 years for Poiana Câmpina, scoring 15 goals in 60 games, helping the team getting a top 10 finish in both seasons.[1]
He then attracted the interest of Petrolul Ploiești in Divizia A, the best team from the Prahova county, three-time champions of Romania. At Petrolul Ploiești he established himself as an important striker in the Romanian league, scoring 27 goals between 1999 and 2002. During his time at Petrolul Ploiești he caught the eyes of Romanian greats Steaua București and Dinamo Bucuresti.[1]
After his experience at Petrolul Ploiești, he changed the team but not the city, signing for Astra Ploiești, where he had a prolific season, scoring 10 goals in 26 games, helping them to a record-high 9th position in Divizia A.[1][2]
After his short spell at Astra Ploiești, he returned to Petrolul Ploiești, where he played for another 2 years, scoring 9 goals in 36 games.[1][2]
In 2004, he transferred to a well-established club in Romania, FC Argeș Pitești, 2-time champions of Romania and the team that gave players like Nicolae Dobrin, Adrian Mutu, Adrian Neaga, Dănuț Coman and Paul Codrea. But, unfortunately for him, his time at FC Argeș was not one of the best, managing to score just 2 goals in 1 season.[1][2]
He was transferred in 2006 by Divizia A newcomers Unirea Urziceni, who were in need of an experienced man upfront. Unirea proved to be a surprise-pack, finishing 10th in the league, and Daniel scored 2 goals for his new team.[1][2]
After his season at Unirea he transferred to Ceahlăul Piatra Neamț.[1][2]