Born in Whyalla, South Australia to Scottish parents, Edwards' family moved to Kwinana when he was a child, where he joined the local junior team before representing Western Australia in a team that won the 1986 Australian under-18 title. He made a couple of appearances for the state senior side at the age of 17, before attending the Australian Institute of Sport in Canberra.
Rangers
In 1988, Alistair then had a spell with Rangers in Scotland.
After returning from his loan spell at Brighton & Hove Albion, Alistair joined Singapore FA in 1990 where he form a potent partnership with compatriot, Abbas Saad which resulted to a strong finished in the league and cup, by finishing runners up to Selangor in the Semi-Pro League 1 and runners up in the Cup final in 1990. Alistair also finished as the league top scorer which he won the golden boot with 13 goals.
Johor FA
After a successful spells at Singapore FA, Alistair joined Johor FA the following year where in his first season, he guided the club to a domestic double winning both the 1991 Liga Semi-Pro Divisyen 1 and the 1991 Malaysia Cup.
Return to Singapore FA
After two successful season at Johor FA, Alistair returned to Singapore FA in 1993.
Midway in 1994, after four years being in Asia, Alistair was transferred to Millwall ahead of the 1994–95 Division 1 season signing a two years contract.
In 1997, Alistair returned to Malaysia to joined with Sarawak FA. In his first season at the club, he helped them to win the 1997 Liga Perdana.
Perth Glory
In 1998, Alistair returned to Australia to joined Perth Glory for whom he played 93 times and scored 24 goals. At the end of 2004, Alistair announced his retirement from football where In all, he made 173 appearances in the National Soccer League for the club.
Alistair was then announced as the head coach of the newly created Australian side, Western Waves but limited resources forced them to dissolvement the following year.
From 2006 to 2009, Edwards became the Football Federation of Australia Development and High Performance Consultant where his main tasks included conducting research in Japan, the Netherlands, France and England on Talent Development and Identification as part of the FFA Development Review and to assist in the development of the FFA National Curriculum. Edwards, along with Paul Okon and Alex Tobin was awarded one of the inaugural FFA Elite Coach Development Scholarships in 2008. As part of his scholarship he spent one month in the Netherlands on attachment with Louis Van Gaal at AZ Alkmaar and Han Westrhoff at Vitesse Arnhem.
Australia Women's
Upon his return, Alistair took the Matildas to the 2008 AFF Women's Championship in Vietnam where they won the tournament. Edwards is also an AFC/FFA Advanced Licence Coach Instructor and conducts Advanced Pathway coaching courses for the FFA. In 2008, Edwards was invited to Cambodia to conduct an Elite Coach Development Course on behalf of the Australian Sports Commission. In August 2009, Edwards was appointed to the position of FFA Assistant Technical Director working alongside Dutchman Han Berger. His dual role at the FFA included the assistant coach role to the Young Socceroos where he worked alongside Jan Verslijen, the head coach of the AIS, U/17 and U/20 national teams.
Perth Glory
In February 2013, Alistair was named the interim manager of Perth Glory after previous manager Ian Ferguson was sacked. Edwards managed his former club for the rest of the 2012–13 A-League season taking them from last position on the table to qualify for the A-League finals.[2] Alistair then was appointed as the permanent head coach of Perth on a three-year deal.[3] On 17 December 2013, Edwards was sacked after a falling out with several players and Perth Glory owner Tony Sage. Senior players, including Jacob Burns, were reportedly upset over being left on the bench due to Alistair' insistence on implementing the club's Western Australia focused youth policy, including usage of his two sons, Cameron and Ryan Edwards, at the expense of other players.[4][5]
In January 2016, Alistair, who was himself a former Johor striker in their historic double-winning team of 1991, was appointed as JDT's Sporting Director[7]Johor Darul Ta'zim is a Malaysian-based football outfit that has enjoyed much success coinciding with Alistair's appointment, although it is mostly attributed to its owner, the Crown Prince of Johor, Tunku Ismail Sultan Ibrahim.
In August 2017, Alistair was reassigned as the club's technical director, responsible for all the developmental teams under the JDT umbrella.[8]
In January 2023, Alistair got promoted to the club chief executive officer while Martín Prest will take on his former role.
Post-retirement
Whilst playing for Perth Glory, Edwards graduated with an MBA from Edith Cowan University and also entered Local Government Politics when he was elected onto the Cockburn City Council from 2002 to 2006.
Since retiring as a player, Edwards has undertaken a number of roles in sport development. He worked as a Sport Consultant at the Western Australian State Government Department of Sport and Recreation from 2002 to 2005 and has since become heavily involved in the development of football in Australia. He commentated A-League games covered by Perth radio station 90.5fm.
In May 2015, Alistair was appointed as the football commentary for Astro Arena until August 2017 where at that time, he was the Sporting Director of Johor Darul Ta'zim.
His son, Ryan was born in Singapore. Despite having been in the country for around 10 days after his birth, he was called up for national service for Singapore on his 18th birthday.