The Swiss world number eight opened the season-ending tournament in London on Monday by beating Berdych 6-3 6-7(0) 6-3.
"It was a dream come true to win on my debut here," Wawrinka told Sky Sports News.
"I have watched many times on TV and today I was here on court. I'm happy to get the win. It's never easy on your first time here but I'm happy with way I played today.
"It's only one match - I take it match after match. I know how I can play and now I'll get ready for the next one."