The ban was due to Russia's invasion of Ukraine, which Moscow calls a "special military operation", and it resulted in ranking points being taken away from the event by the ATP and WTA Tours.
As part of their return, players from the two nations are playing as neutrals and are not allowed to receive state funding or have sponsorship from Russian or Belarusian companies.
Britain is a major ally of Ukraine and continues to provide military support but there was no animosity from the crowd towards former world number one Azarenka as she edged past China's Yuan Yue 6-4 5-7 6-4 in the first round.
"Honestly, it was really nice. People are very nice. I feel like there is an online part of it and there is the aura, and for me personally, I experienced very good treatment," the 19th seed told a press conference.
"There are of course some incidents sometimes happens (at other events), but I felt like I was very welcomed everywhere. I have been very supported everywhere. And I really appreciate that part.
"Today to hear people say, 'Let's go, Vika' and cheering me on was also why I play, to play in front of the crowd, to put on a good show. So that felt great."
Azarenka's compatriot Aryna Sabalenka skipped two press conferences at the French Open last month citing mental health reasons after being grilled about the invasion of Ukraine and Belarus being used as a staging ground for Russian troops.
The world number two begins her Wimbledon campaign against Hungary's Panna Udvardy on Tuesday.