[2] As an "Aris kid" playing for his beloved club, but also with the fact that he experienced dark days as well as lighter, he was one of the fans' favourites logically, also one of the "last Mohicans" in the club ("Mohicans"- figuratively related to the players as Giorgios Koltsidas, Kostas Nebegleras, Papadopoulos, Georgios Gougoulias, Ronald Nacho Garcia, Efthimios Kouloucheris, Kristi Vangjeli, Petros Passalis, Spyros Gogolos, that were with this team in the second division, season 2005/06, as well as the season's after that, when the club experienced its promotion and then a total rebirth in the first division with good football and higher standing positions).

Also as stories were circulating during the season (2006/07), he had been watched closely by some bigger clubs' scouts like Benfica or Chelsea, and Zenit of Russia as well.

His partnership with Olof Mellberg at the centre of defence played a vital role for Olympiacos as they won back-to-back championships in the 2010–11 and 2011–12 seasons.

On 24 June 2011 he was accused by the Athens prosecutor for his alleged involvement in match-fixing, as the list of those implicated in the scandal that has rocked Greek football grew.

Papadopoulos, who plays for champions Olympiacos, was also included in the list along with another high profile player, Kostas Mendrinos, who is on the books of Aris.

After an eight-month absence, Papadopoulos returned to play by entering as a substitute for Kostas Manolas on the 46th minute of a 1–0 victory over Kavala F.C.

The Greece international took the time to praise Olympiacos president Evangelos Marinakis, but revealed that his relationship with Spanish coach Michel was beyond repair after completing his move to Turkey.

Papadopoulos was set to be the center of fans attention, with the veteran midfielder becoming only the second Greek player to play in Turkey's top-flight, following Theofanis Gekas.

On 15 August 2015, in an away 2–2 draw against the champions Guangzhou Evergrande, he managed to score the second goal, helping his club to avoid defeat.

[11] On 20 February 2016, due to the reorganization of the team and the acquisitions of Demba Ba and Obafemi Martins in combination with the limitation of foreign players, forced the Greek international to dissolve his contract with the club.

[12] On 23 February 2016 it was rumoured that Atromitos were interested in signing the central defender who was recently released by Shanghai Greenland Shenhua.

Melbourne-born Papadopoulos played seven games at centre-back during the semi-finalists' 2016–17 season, providing cover for Luke De Vere and Jade North.

[18] On 28 October 2017, Wellingthon's keeper Smith failed to properly deal with a Fahid Ben Khalfallah free-kick, with defender Papadopoulos taking the rebound on the spot to score his first A-League goal,[19] in a 3–3 away draw.

On 17 November 2017, Papadopoulos scored the opener and the clincher for the Brisbane Roar as they climbed off the bottom of the ladder in a 3–1 home win game against Melbourne City FC.

The incident saw the Roar make a statement shortly after the game panning the actions of Avraam that marred the club's 3–1 A-League loss, against Sydney FC.

[22] On 8 December 2017, Papadopoulos was given a seven-match ban by the A-League judiciary for spitting on Sydney FC's Matt Simon.

The defender's ban included the one match he had already served, when he sat out the Roar's 2–0 win over Western Sydney Wanderers FC.

[24] A week later, Papadopoulos scored, he put the hosts ahead and kept their slim A-League finals hopes alive with a 3–2 win over fellow battlers Perth Glory.

[27] On 28 January 2019, Olympiacos revealed that veteran defender Avraam Papadopoulos has returned to the club for a six-month contract.