Moffat was born and raised in Falkirk, Scotland. The first album he bought was Elvis Sings For Kids by Elvis Presley. Whilst at Falkirk High School, he listened to such bands as Pixies, Dinosaur Jr. and Slint. His first ever gig was at age 16, and saw David Byrne at the Glasgow Barrowlands in 1989. In 1990, at age 17, he was expelled from school, with no Higher Qualifications. He then worked for four years at an independent record shop called Sleeves Records, resigning one morning in 1996, due to having a hangover and wanting to go home.
In 1995, Moffat and Malcolm Middleton began making music under the name Arab Strap and sent in demo cassettes to record companies. Only one, Chemikal Underground, replied, and they were soon signed to them.
Moffat and Middleton briefly reunited in November 2011 for a gig as part of the 20th anniversary celebrations of Glasgow venue Nice N Sleazy.
In 2002, after being challenged by Malcolm Middleton to release a solo album, Moffat released a solo album entitled Hypnogogia under the name Lucky Pierre. In 2005, after changing the name to L. Pierre, Moffat released an album called Touchpool. In 2007 he released Dip.
From 1991 to 1996, Moffat recorded with a band called The Angry Buddhists, which consisted of Aidan Moffat, Gavin Moffat, Stuart the Postman, "Cheg" Taylor and The Stobe. They recorded "over 40 songs on dictaphones and 4-tracks", but never played live. Moffat was also the drummer in Bay, a band who released two albums – Happy Being Different (1994) and Alison Rae (1995).
Moffat provided guest vocals on the Mogwai song R U Still in 2 It from Mogwai Young Team, recorded in the same studio (MCM Studios in Hamilton) around the same time as Arab Strap were recording The Week Never Starts Round Here in 1997. Moffat also contributes vocals to the Mogwai song Now You're Taken from 4 Satin. Mogwai have a song dedicated to him on their second album, Come on Die Young, entitled "Waltz for Aidan".
In 2002, Moffat, Stuart Braithwaite from Mogwai and Colin "Sheepy" McPherson released an eponymously titled EP under the name "The Sick Anchors".
Moffat uses his own name for his 2007 poetry album, I Can Hear Your Heart.
Aidan Moffat & the Best-Ofs are a four-piece band fronted by Moffat. They played their first gig supporting American band Slint at the Glasgow ABC in Scotland, where they debuted the songs "Big Blonde", "The Last Kiss", "Ballad of the Unsent Letter", "Living With You Now" and "Atheist's Lament". Their first album, titled How to Get to Heaven From Scotland, was released on 3 March 2009.
In 2009 Moffat wrote an advice column for the online magazine The Quietus.
In 2011 Moffat and pianist, bassist and former Arab Strap collaborator Bill Wells released Everything's Getting Older, which in June 2012 won the first Scottish Album of the Year (SAY) Award from the Scottish Music Industry Association.
In early 2013 Moffat released a new L. Pierre album, The Island Come True. In July he released another full album, The Eternalist, which was made available for free online and recorded on Vine.
In 2016 Moffat featured in the documentary 'Where You're Meant To Be', in which he toured Scotland performing his reinterpretations of traditional Scottish folk songs. The film also features the traditional singer Sheila Stewart who is critical of the project, viewing it as disrespecting the tradition, but who ultimately performs alongside Moffat in a performance at the Glasgow Barrowlands.
Moffat lives in Glasgow with his partner and two children, a boy and a girl.
He is known for his distinctive facial hair, which he has commented on, sayingHypnogogia (as Lucky Pierre) Melodic 2002
Touchpool (as L. Pierre) Melodic 2005
Dip (as L. Pierre) Melodic 2007
I Can Hear Your Heart Chemikal 2007
Everything's Getting Older (with Bill Wells) 2011
The Island Come True (as L. Pierre) 2013
The Eternalist (as L. Pierre) 2013
The Most Important Place in the World (with Bill Wells) 2015
Where You're Meant To Be (Live Album) 2016