The 35-year-old was detained and then deported from Australia last January in a dramatic process after trying to enter the country without having a Covid-19 vaccination.
He was subsequently given a three-year visa ban, but the Australian government has since overturned, freeing him up for a return to Melbourne Park in early 2023.
Djokovic was delighted to receive the news on Tuesday and celebrated with a 6-4 6-1 win over Andrey Rublev in the ATP Tour Finals in Turin, which booked his place in the last four.
The Serbian said: "I was very happy to receive the news yesterday. It was a relief obviously knowing what I and the people closest to me in my life have been through this year with what happened in Australia and post-Australia.
"I could not receive better news for sure - during this tournament as well.
"Did it affect my game today? I would like to believe it did. Why not? I don't think it did affect me too much because I'm familiar with what I need to do in order to prepare myself for every match.
"Of course, knowing that I have clarity now, what I do in the off-season, starting the season in Australia, also of course it did relieve some of the pressure me and my team felt. Just giving that clarity makes it great for us.
"Australian Open has been my most successful Grand Slam. I made some of the best memories there. Of course, I want to go back there, I want to play tennis, do what I do best, hopefully have a great Australian summer.
"I'm always thankful to go through experiences, no matter what the experiences are. I try to be optimistic and positive in life. I look forward to starting the new year in Australia, and we'll see how the next year goes."
Djokovic put in a flawless display against Rublev to make it through to the last four for the 11th time at the end-of-season event.
Stefanos Tsitsipas and Daniil Medvedev meet later on Wednesday, with both men having lost their first match.
Briton Neal Skupski and his Dutch partner Wesley Koolhof lost 6-4 7-6 (3) to Croatian powerhouses Nikola Mektic and Mate Pavic in their doubles rubber.