In 1975, Stoica transferred to giants Steaua Bucharest, where he played fourteen seasons and helped win the league title in 1976, 1978, 1985, 1986, 1987, 1988 and 1989, and the Romanian Cup in 1979, 1985, 1987, 1988 and 1989. He was also part of the Steaua squad that defeated FC Barcelona in the 1986 European Cup Final, adding the subsequent European Super Cup.
In 1989, Stoica played for a season for Ligue 2's RC Lens, and after one more game with Steaua in 1991 he called it a day. He is the player with the most games played for Steaua - 369, during his 14 seasons with the team. He was also the team captain for many years.
On 25 March 2008 he was decorated by the president of România, Traian Băsescu with Ordinul "Meritul Sportiv" — (The Order "The Sportive Merit") class II for his part in winning the of 1986 European Cup Final.