Anastopoulos was born on January 22, 1958. He started his career at Dafni before transferring to Panionios with whom he debuted in the Alpha Ethniki in the 1978 season. Thanks to Anastopoulos, Panionios won the Greek Cup in 1979 upsetting AEK 3-1. His debut in European competition was also impressive as he scored twice against Twente Enschede of Holland and once against IFK Goteborg in the Cup-winners' Cup. His performance brought an immediate transfer offer from Twente as well as other Greek and foreign clubs. Finally, in 1981, he went to Olympiakos Piraeus.
As an Olympiakos player, Anastopoulos, also known as "Moustakias" (the moustachioed one), won top scorer honours in 1983 (29 goals), 1984 (18 goals), 1986 (19 goals) and 1987 (16 goals). His goal-scoring exploits in 1983 won him the Bronze Boot as third scorer in all Europe.
In 1988, Anastopoulos left Greece to play for Avellino in Italy. Though he performed well in the Italian Cup, he failed to score a single goal in Serie A' and returned to Greece when Avellino were relegated.
After coming close to signing with AEK, Anastopoulos chose to return to Panionios. He later played for Olympiakos, Ionikos (1993) and closed out his career with Olympiakos (once more) after the 1994 season.
During his playing career Anastopoulos was capped 75 times by the National Football Team of Greece scoring 29 goals - more than any other Greek international. He was a member of the Greek squad in the finals of Euro 1980 and scored the lone Greek goal of that competition with a brilliant header against Czechoslovakia.
After his playing career was over, Anastopoulos coached a variety of clubs:
- Panelefsiniakos (1997)
- Kallithea FC
- Kerkyra FC (2005)
- Aris (2006)
- Kavala FC (2008 - 2009)
- PAS Giannina (1999, 2004, 2007, 2010)
- OFI (2010 - 2012)
- Atromitos (2012–13)
- Platanias (2013–14)
- Panionios (2014)
- OFI (2015)
- Aris (2015–17)