Stoltidis started his footballing career with the club Iraklis before moving to Olympiakos in the year 2003. Ieroklis Stoltidis was signed to replace Zé Elias at Olympiacos CFP and adds an extra dimension with his heading ability from set-pieces.
Stoltidis started out at Pontioi Kozanis in the fourth division before signing for Iraklis FC, where he spent eleven years. He made his Alpha Ethniki debut for the Thessaloniki-based club in December 1992 but did not become a regular until 1995/96. The following term he played UEFA Cup football for the first time. Stoltidis stood out in 2002/03 and was named the club's player of the season. In June, after 234 league matches, he left for Olympiacos CFP, signing a two-year contract.
Crucial goals against eventual champions Panathinaikos FC and AEK Athens FC in 2003/04 endeared him to supporters. Stoltidis also relished his first taste of UEFA Champions League football, scoring twice in five appearances.
A regular in Dusan Bajevic's side in 2004/2005, he played 25 league matches and scored twice. He appeared in all 540 minutes of the Champions League campaign and scored the winner at home against eventual champions Liverpool FC. In the same season, he won the Alpha Ethniki as well as the Greek Cup with Olympiakos.
During the 2005/06 season, he started in the first eleven in the Greek El Clasico, Panathinaikos vs Olympiakos, and went on to score in Olympiakos' 0-2 victory. In Norway, Stoltidis is mostly famous for a violent tackle on Per Ciljan Skjelbred, which broke the 18-year-old's tibia and fibula and almost ended his career. Stoltidis finished the 2005/06 season with another Olympiakos double as well as the award for Greek Footballer of the Year.
The 2007/08 season would once again prove successful for Stoltidis. One half of Takis Lemonis' defensive midfiled duo, Akis formed a strong partnership with Argentine International Cristian Raul Ledesma. Stoltidis also continued his streak of Champions League success, this time helping Olympiakos finish second and gaining entry into the Round of 16. Finishing the group stages with 3 goals and 2 assists, Stoltidis pulled off some of the most memorable performances of his career, most notably the 1-3 and 3-0 victories against SV Werder Bremen where Stoltidis found the back of the net 3 times.
Stoltidis was a member of the Greece side defeated in the 1998 UEFA European Under-21 Championship final by Spain. In November 1999, he made his debut for the senior national team and he went on to represent Greece at the Athens Olympics in 2004. Despite performing at an incredibly high rate for his club Olympiakos, Greece National Team coach Otto Rehhagel left Stoltidis out of the UEFA Euro 2004 championship winning squad and did not feature Ieroklis in any of the qualifying matches for the FIFA World Cup 2006 or UEFA Euro 2008 campaigns. Finally, after years of media speculation, Stoltidis was called to the National Team under Rehhagel for a friendly against the Czech Republic. This call however came too late in Stoltidis' opinion, as Akis respectfully declined the invitation stating "I'm no longer at an age where I can perform on all those fronts at the required level. Apart from my gratitude to the fans for their support, I want to assure them that, had this call come earlier in my career, when I was capable of competing on all fronts at a high level, I would have put myself at the disposal of the coach without hesitation."