For most of his career, Coventry-born Alexander played as a specialist at right back, but was also deployed in defensive midfield, as he did early on in his career with Scunthorpe. He is the fourth oldest player to score in Premier League history. He was also a penalty kick specialist. On 16 April 2011, in Burnley's win over Swansea City in a Championship match, Alexander became only the second outfield player in English football history to have made 1,000 professional appearances, after Tony Ford. He is fifth on the list of footballers in England and Scotland by number of league appearances.
Alexander was appointed manager of Fleetwood Town in December 2012. He won the 2013–14 League Two playoffs and promotion to League One, but was sacked by Fleetwood in September 2015. In March 2016, he was appointed the manager of Scunthorpe United.
Alexander began his career in the late 1980s as a youth player with Scunthorpe United. He made his first-team debut on 27 April 1991, coming on as a substitute for Mark Hine, and signed his first professional contract the same year. In 1991–92, he established himself as a member of Scunthorpe's first team, usually playing at right back.
Alexander made over 200 appearances at Scunthorpe before moving to Luton Town for a transfer fee of £100,000. He went on to make a similar number of appearances with Luton in his four years with the club.
In 1999 two clubs were vying for his signature; Burnley and Preston North End. Both clubs made offers for the player but Alexander opted for a move to Preston. He became a first team regular at Deepdale, eventually club captain and an established set-piece taker, particularly in penalties. Alexander stayed remarkably fit during his career, hardly ever suffering a major injury. However, during the 2000–01 season, Alexander missed several weeks of the season after breaking his rib in an away match against Wolverhampton Wanderers. During his eight years at Preston, Alexander made exactly 400 appearances for the club, with his 400th and final match coming against Colchester on 25 August 2007. He was also in the PFA's Championship Team of the Season for 2004–05
During the summer of 2007 a number of clubs were linked with Alexander including Crystal Palace who had a £50,000 bid turned down by Preston, who said;
"He is club captain and a vital member of this squad and certainly not a player we will allow to leave."
On 29 August 2007, he made a surprise move to local rivals Burnley almost nine years after they had originally tried to sign him. The reasons cited for his departure were that Preston would not extend his contract by another year, so when offered a two-year contract by Burnley the player accepted and made a £200,000 move to Turf Moor. Preston Chairman Derek Shaw did not want to lose the player and said;
"We don't particularly want to sell Graham but he has the comfort of a two-year contract at Burnley whereas he only has one year here at Deepdale. We quite possibly would have renewed Graham's contract, he's a fit man."
The £200,000 transfer money was made up of £100,000 payable in 2007 and the final £100,000 payable in the summer of 2008.
In Burnley's promotion season in 2008–09 Alexander at the age of 37 played in all of Burnleys 61 League and Cup games that season ending with the 1–0 Play-Off final victory over Sheffield United at Wembley which took Burnley back to the Top Flight of English Football for the first time in 33 years.
On 29 June 2009, Alexander signed a new one-year contract at Burnley, and on 15 August he became the oldest player to make a Premier League debut. On 19 September, Alexander scored his first Premier League goal, a penalty, in a 3–1 win at home to Sunderland. On 31 October 2009, Alexander scored both goals in a 2–0 home win against Hull City. A week later he then scored the first for Burnley, from the spot, at Manchester City in a thrilling 3–3 draw. On 16 December, he scored his 100th league goal. He scored an equaliser against Arsenal, sending Gunners 'keeper Manuel Almunia the wrong way. On 10 April 2010, Alexander again scored twice against Hull City – both penalties – in a 4–1 win to take his tally for the season to eight, seven of which have been penalties. Alexander takes penalties in an unusual way, opting to use the outside of his foot rather than the inside. On 6 May 2010 he was named Burnley's Player of the year for the 2009–10 season. He is among the oldest players ever to score in the Premier League.
On 5 August 2010 Burnley's First Team Manager, Brian Laws, officially named the 38-year-old as club captain for the 2010–11 season. On Alexander's appointment, Laws said "Graham is the consummate professional who has been instrumental in the success that this club has seen in the past few seasons, so it was an easy choice"
In April 2011, Alexander made his 1,000th senior appearance for club and country in a 2–1 win against Swansea City as an 87th-minute substitute. Only Tony Ford has matched this feat as an outfield player. At the end of the season, Alexander looked likely to leave Turf Moor, as he was linked with managerial jobs with Bury and Macclesfield Town, but Burnley boss Eddie Howe stated that he was still part of his plans for the following season. On 4 July 2011, Alexander was released by Burnley.
Alexander returned to Preston North End on 3 August 2011, as he signed a one-year contract with the club. He was given the number 22 and made his debut against Colchester United.
Alexander scored his first goal for Preston in 4 years with a trademark penalty in a 2–1 home win against Tranmere on 24 September 2011. This was after his first penalty back in a Preston shirt was saved by Exeter's Artur Krysiak, and before his third was saved by Lee Butcher of Leyton Orient. His next penalty came in a penalty shootout against Rochdale in the Football League Trophy, which was slotted into the top corner after he was brought on as a substitute for Conor McLaughlin especially to take a penalty in the shootout. However, he missed his next penalty, again in the JPT, and again in a penalty shootout, this time against Chesterfield. He was the third Preston player to take a penalty in this shootout, and he blazed it over the bar, much to the disbelief of the fans. Preston's next penalty-taker, Paul Coutts, had his penalty saved, and then when the next penalty was scored by Chesterfield's Alexandre Mendy, Preston got knocked out of the tournament. Alexander started the next league game against Stevenage but was replaced through injury by Steven Smith after just 3 minutes, after which Alexander did not feature for the Lilywhites for a long time, and there was speculation that he had played his last game for Preston, and in his career.
After the sacking of Phil Brown a few games down the line, he became joint-caretaker manager, alongside David Unsworth. His first match in joint-charge was an away match against MK Dons, which they won 1–0. Just before what was to be an ordinary match against Wycombe Wanderers, it was announced that Graham Westley would replace them at the helm of Preston, and that Wycombe was to be the last match in charge for the pairing of Alexander and Unsworth. They won the match 3–2, and left a good base for Westley to build on.
Playing his final game on 28 April 2012 against Charlton Athletic, Alexander came on as a substitute for Max Ehmer in the 84th minute. This was supposed to be a cameo appearance to allow the Preston supporters to show their appreciation of his service to the club. However, with Preston losing 1–2 in stoppage time, they were awarded a free-kick 25 yards from Charlton's goal. Alexander stepped up to curl the ball around the wall and inside the near post, scoring with the very last kick of his career.
On 20 June 2012, Alexander was appointed Head of Youth Development. Chairman Peter Ridsdale said "He's got over 1,000 games under his belt, he's a hero here and what better person to head our youth development."
In July 2013 Alexander was voted Preston North End's greatest ever right back by the fans.
Born in England to a Scottish father, Alexander was eligible to play for either England or Scotland. Before his first international call, Alexander said, "To be honest, since I started playing football, I've had two ambitions: to play in the Premier League, and to play for Scotland. I've been brought up supporting Scotland as far back as I can remember." This ambition was fulfilled when he made his Scotland debut on 17 April 2002 in a 2–1 friendly defeat to Nigeria at Pittodrie Stadium. Alexander was part of the Scotland squad who won the annual Japanese Kirin Cup tournament in 2006, beating Bulgaria 5–1 before drawing 0–0 with Japan. He gained his 25th Scotland cap in a famous 1–0 victory against France. He gained a total of 40 caps for Scotland. Alexander was shown only one yellow card while playing for Scotland, against New Zealand in May 2003.
Alexander was appointed manager of Fleetwood Town in December 2012. Fleetwood were seventh in 2012–13 Football League Two when he was appointed, but had just been eliminated from the 2012–13 FA Cup by Aldershot. He guided Fleetwood to promotion in 2013–14 by winning the League Two play-offs, but was sacked in September 2015 after a poor start to the 2015–16 Football League One season.
Alexander was appointed First Team Manager of Scunthorpe United on 22 March 2016.
As of match played 17 September 2017