After playing six seasons for Universitatea Craiova, Popescu was loaned to Romanian giants Steaua Bucharest reaching the semi-finals of the European Cup during their 1987–88 campaign. He moved abroad to the Netherlands in 1990, and signed for PSV Eindhoven at the request of Sir Bobby Robson, helping them to keep among the top Dutch sides, until he was transferred to Tottenham Hotspur in the Premier League on 9 September 1994 for a fee of £2.9million. He played 23 times in the Premier League and scored three goals as Spurs (who changed manager from Ossie Ardiles to Gerry Francis a few weeks after Popescu arrived) finished seventh in the league – their highest finish for five years. He also helped them to reach the FA Cup semi-finals, where they lost 4–1 to eventual cup winners Everton. However, after less than a year in England, he left Tottenham to sign for the Spanish club Barcelona for £3million, succeeding Ronald Koeman in the team. He was made captain of the Catalan club, contributing to their Copa del Rey (domestic cup) glory in his first season and their UEFA Cup Winners' Cup triumph in his second.