By his own admission, the Dutchman had struggled to adapt to life with Inter - both on and off the pitch - yet he was still a striker that had won numerous honours in his native Netherlands and Italy, as well as making major contributions at international level.
From his debut in the home encounter on the opening day of the campaign against Middlesbrough, Bergkamp's class was there for all to see. While Ian Wright was a proven scorer of goals, the new £7.5m signing provided a touch of class and creativity to Arsenal's frontline.
However, among other duties, centre-forwards must score goals, which is something that Bergkamp struggled to do initially. In his first seven encounters in all competitions, he failed to find the net, which led some in the media to brand him a flop, while opposition fans chanted 'what a waste of money' in his direction.
In Bergkamp's biography, Stillness and Speed, his former teammate Wright takes up the story: "When Dennis started at Arsenal he didn't start great. There were murmurs from the fans and I remember him getting stick from a player from Hartlepool. This player from fucking Hartlepool was saying stuff to Dennis! I kind of took it personally myself. Dennis was playing well, but for some reason goalies were making saves against him or whatever."
But, in what was his eighth outing in an Arsenal shirt, Bergkamp finally silenced the critics as Southampton visited North London 19 years ago today.
The fixture was just 17 minutes old when the moment arrived. Glenn Helder used his pace to get down the left flank, before sending a deep cross over towards the back post for his compatriot, who sent a low volley into the bottom corner of Dave Beasant's net.
Reflecting on that moment, Bergkamp, again in Stillness and Speed, recalled: "The way the crowd reacted was more than I could have imagined. I wouldn't say it was typically English but the way they celebrated, all jumping up and hands in the air together...it's not explosive like that anywhere else.
"That moment was the start of the relationship with the Arsenal crowd. They'd been patient with me, and I didn't know why because they didn't know me. Maybe they saw something in the games leading up to that goal? It must be something like that because I seemed to have built up a lot of credit very quickly. After that goal we never lost that relationship."
Tony Adams made it 2-0 to the hosts soon after, but the visiting Saints were level before the break thanks to efforts from Gordon Watson and Ken Monkou. Just like London buses, though, Bergkamp was on hand to put the Gunners back in front in the 68th minute.
After he had inherited possession just inside the Southampton half, Bergkamp carried the ball forward, beating Neil Maddison along the way. Then, as he progressed towards the edge of the area, he unleashed a powerful shot that flew in via the upright. Wright then sealed the outcome 17 minutes from time when he added a fourth for the hosts.
That brace of goals were to be the first of 120 that Bergkamp would score during his 11-year career with Arsenal.
ARSENAL: Seaman; Dixon, Bould, Adams, Keown, Winterburn; Parlour, Merson, Helder; Wright, Bergkamp
SOUTHAMPTON: Beasant; Dodd, Monkou, Hall, Benali; Widdrington, Maddison, Magilton; Le Tissier; Shipperly, Watson