Basinas started his career with Greek side Panathinaikos, during his time at Panathinaikos he won both the league and the Greek Cup in 2004. After a row broke out between Basinas, the manager and the Panathinaikos board over wages, Basinas was released on 21 September 2005, which brought an end to a career at the club which lasted over 10 years, during this time he made over 150 appearances for the club scoring many crucial goals both domestically and in European competitions. ( He played 153 games (26 goals, 5 assists) with the club in all competitions).
Although rumored to go to Birmingham City, Everton, AEK Athens and Olympiacos during the 2006 Winter transfer window, Basinas signed a contract with Mallorca preferring to leave Greece and join the Spanish Primera División. In the second half of the 05/06 season, Basinas completed a successful first period at Mallorca, helping to save the team from relegation proving a key part of the struggling teams survival. In his second year at the club he helped the team to finish in 7th position, one point from European qualification. He was released by Mallorca on 1 July 2008 after his 2½ years' contract came to an end. He played 81 games (1 goals, 1 assists) with the club in all competitions.
On 31 July 2008 he signed a 3-year contract of €1.4 million per annum with AEK Athens, choosing the number 14. Despite the pre-season odds, AEK underachieved during the first half of the season and lost the title race too early, making Basinas favourable towards a new move during the winter transfer period.
On 2 February 2009, Portsmouth confirmed the signing of Basinas on an eighteen-month contract. He made his debut for Portsmouth on 7 February 2009 against Liverpool. Just a few hours after his debut, manager Tony Adams, who brought Basinas in, was sacked by the club and replaced by Paul Hart. Under the new manager, Basinas hardly played and was benched for the rest of the season after only making 3 appearances for Portsmouth. Despite little playing time in his first season at Portsmouth, Basinas stated that he wanted to stay at the club. When Avram Grant became the manager of the club, Basinas had continued to impress for Portsmouth when called upon and a poll among Portsmouth fans on 23 January 2010, showed that he's appreciated by the fans. 77% of fans believe that "Basinas has the creative touch and must play", while only 2% believed he should leave the club. With Portsmouth Angelos Basinas reached the 2010 FA Cup Final against Chelsea of Carlo Ancelotti.
In the summer 2010, Angelos Basinas moved to Arles, with his teammate Angelos Charisteas, in the Ligue 1. He made his debut on 21 August 2010 in a 1–2 away defeat against Toulouse. Basinas made a total of five appearances in League 1 and French Cup. The contract was broken two months later.
Basinas won his first cap in a 3–1 win over El Salvador on 18 August 1999 and scored his first goal in just his second match, also against El Salvador just two days later. He has remained a part of the national team setup since his debut and has been a regular since Otto Rehhagel took over in 2001.
He was a key player in Greece's upset European Championship victory, scoring a penalty in his country's 2–1 upset win over host team Portugal in the tournament's opening game. Basinas was a vital player in the hard working midfield of the Greek team throughout the tournament. In the final, Charisteas scored the winning goal for Greece against Portugal off a corner kick by Basinas, which saw Greece win the trophy.
After Theodoros Zagorakis retired, Basinas was selected to take the captains arm band. Basinas earned his 100th cap for Greece 1 April 2009 in a FIFA World Cup 2010 qualifier against Israel. At the time, he was only the second Greek player to achieve 100 national team appearances alongside Theodoros Zagorakis.
PanathinaikosGreek League: 1995–96, 2003–04
Greek Cup: 2003–04; Runners-up 1997–98, 1998–99
PortsmouthFA Cup: Runners up 2010
Greece U-21UEFA European Under-21 Championship: Runners-up 1998
GreeceEuropean Championship: 2004