The 29-year-old DR Congo international joined Newcastle from Brentford in September for £55 million, but suffered a knee injury while on international duty soon after, delaying his debut.
He came on as a substitute in the 75th minute against Burnley, replacing Nick Woltemade, to a warm reception from the home fans.
"It has been a long time coming," Wissa told the BBC after Saturday's match. "Over the last 11 weeks, I've learned about the team and the players. It has been a long road, but I'm happy in the end.
"It gave me goosebumps (when I came on). I'm buzzing now.
"It can be an excellent season because we have so many quality players."
Newcastle manager Eddie Howe said Wissa, who scored 20 goals and registered five assists in 39 matches across all competitions last season for Brentford, will need time to regain peak fitness.
Newcastle will not have to worry about losing him to the Africa Cup of Nations, as he has not been included in DR Congo's squad.
"A real lift to have such a quality player back into our ranks," Howe told Newcastle in an interview.
"He's quite a long way short of his best physical levels. That's just with the injury that he's had and the time that he's had out. We're going to have to build him up slowly but surely and try and get him back to his very best.
"But a very exciting player to have."
Newcastle are 11th in the league table with 22 points from 15 matches.
Next, they travel to German side Bayer Leverkusen in the Champions League on Wednesday.