Donis was born and raised in Frankfurt, West Germany until he was six years old and the family moved back to their native Greece. His parents had lived in Frankfurt for "many years" and he has still family ties there.
Giorgos Donis started his senior career with PAS Giannina in 1990, and after one successful year he moved to Panathinaikos. The fans of Panathinaikos, known for their love for nicknames, named him the Train for his remarkable acceleration.
On 5 June 1996, after helping the Greek club reach the UEFA Champions League semi-finals against Ajax FC, Donis moved to Blackburn Rovers on a free transfer, making use of the then recent Bosman ruling signing for 1.1 billion drachmas, a record amount for Greek players at the time. He had an erratic season with Blackburn, scoring against Everton and Coventry City. He then headed back home to play for AEK Athens, before moving back to England again, playing for Sheffield United and Huddersfield Town where he ended his career.
He made his debut for the Greek national football team on 22 December 1991, in a 1–1 draw against Malta for the UEFA Euro 1992 qualifying round. He appeared in 24 matches and scored five goals during his international career with Grecce.
After the end of his playing career, he turned to coaching. Starting in 2002, he led Zografou-based Ilisiakos in two consecutive promotions from 4th to 2nd Greek football level. He then made the move to AEL, where after one season he managed to bring the team to the Greek Superleague from the second division and finished them in 8th place the following year. In 2007, Larissa finished only 10th in the league but he managed to bring them the Greek Cup after defeating Panathinaikos 2–1 in the final. In his first taste of European football management, his team AE Larissa defeated his former team Blackburn Rovers to reach the 2007–08 UEFA Cup group stages. He finished a great year in 6th place in the league, missing out on the season play-off's on goal difference.
On 25 April 2008, Donis stepped down as manager of AEL and on May 14 he was appointed as head coach of AEK Athens. On 17 November 2008, due to a string of poor performances and early knock out from the UEFA Cup, AEK parted company with him just six months after his appointment.
In 2009, Donis was appointed by Atromitos and in the 2010–11 season he again reached the Greek Cup Final only to lose 0–3 to his former team AEK Athens. In the next year, Atromitos enjoyed another successful spell under his guidance, reaching the Greek Cup Final for a second consecutive time (losing 1–2 to Olympiacos at extra time), as well as participating at the Greek Superleauge play-offs.
On 31 May 2012, PAOK appointed Donis as the new manager of the club, on a two-year contract, with immediate effect. On 28 April 2013, after a crucial defeat 0–2 and the elimination in the semi-final of Greek Cup by Asteras Tripolis, he was sacked by chairman Ivan Savvidis.
On 11 October 2013, Donis signed a contract until the end of the 2013–14 season with the reigning Cypriot champions APOEL, replacing Paulo Sérgio who had been fired on 4 October 2013. In his first season at APOEL, Donis achieved to win the double. He won his first title with APOEL on 21 May 2014, when he led his team to a 2–0 victory over Ermis Aradippou in the Cypriot Cup final. Ten days later, Donis won also the Cypriot First Division after APOEL's 1–0 away victory against AEL Limassol in the title deciding match and won his first league title in his managerial career.
Following a successful first season in the club, Giorgos Donis signed a one-year contract extension with APOEL on 26 June 2014. In August 2014, Donis led APOEL into the group stages of the 2014–15 UEFA Champions League, after eliminating HJK Helsinki (4–2 on aggregate) in the third qualifying round and trashing Aalborg BK 5–1 on aggregate in the play-off round of the competition. APOEL were drawn in Group F alongside Barcelona, Paris Saint-Germain and Ajax. Donis led his team to some great performances in the group stage, but APOEL managed to collect only one point after drawing 1–1 with Ajax at home. In their other five Group F matches, APOEL lost twice to Barcelona (0–4 at home, 0–1 away), lost twice to Paris Saint-Germain (0–1 at home, 0–1 away) and also lost to Ajax 0–4 away.
On 6 January 2015, APOEL and Giorgos Donis parted company by mutual agreement after a poor run of performances and results, culminating in a 1–1 home draw against the last-placed Ayia Napa.
On 25 February 2015, he was appointed as the new manager of Al-Hilal in Saudi Arabia, signing a contract until the end of the season. He helped Al-Hilal to qualify in the semi-final of the 2015 AFC Champions League. On 6 June, Donis won the first title with Al-Hilal after defeating Al-Nassr in the final of the 2015 King Cup of Champions.
On 28 July 2016, he was appointed as the new nanager of Al-Sharjah in UAE, signing a contract until the summer of 2018.As of 13 September 2017
Greek League: 1994–95, 1995–96
Greek Cup: 1992–93, 1993–94, 1994–95
Greek Super Cup: 1993, 1994
Greek Cup: 2006–07
Greek Second Division: 2004–05
Greek Cup: Runner-up 2010–11, 2011–12
Gamma Ethniki: 2003–04
Delta Ethniki: 2002–03
Cypriot League: 2013–14
Cypriot Cup: 2013–14
King Cup of Champions: 2015
Saudi Super Cup: 2015
Saudi Crown Prince Cup: 2015–16