But the former right-back also had to overcome setbacks, including a 2-1 extra-time defeat to Manchester United in an epic FA Cup semi-final replay in 1999.
Speaking in the seventh part of "Inside Matters", a series of exclusive interviews with football stars about the mental challenges they have faced, Dixon talks about how he felt after Ryan Giggs' stunning solo goal helped put Man Utd on their way to an historic treble and how he dealt with the Gunners finishing the campaign without any silverware.
"I didn't think I was ever going to get over that," says Dixon. "I remember that summer I wasn't a particularly happy chap.
"I think we had about five weeks off before we were back training. I was miserable."
Dixon believes it is best to avoid dwelling on difficult situations and that we should attempt to stay in the moment as much as possible.
"It's definitely a similarity with life when we have our dark moments when we are sitting at home and things are not going great for whatever reason," he says.
"I've always been taught by my dad, which helped me in these moments, is that when things are really good they are never quite as good as you think, and likewise when things are bad, you can just lift your head above that parapet and go, 'They're not as bad as you think'.
"That's the message I was trying to send out to anybody, young players, young athletes, people in any walks of life. To just try to stay in the moment and live the day that you're in because we haven't got anything else and the important thing right now is to take every day at a time."