The 25-year-old re-signed for the Serbian giants last week, six months after leaving the club for Chinese outfit Jiangsu Suning.
He netted 39 times in 48 competitive games for The Stars during his first spell between 2017 and 2018.
''I am grateful to everyone who enabled me today to be with Red Star Belgrade and everyone who helped in the qualification [Champions League]," Boakye said at his unveiling on Tuesday.
''I am happy that my teammates managed to reach the group phase [of the Champions League]. I was happy reading with the two away goals scored at [Red Bull] Salzburg [in the play-off round to seal qualification on away goal rule].
''However, I did not come because we qualified, but to enjoy football. I would like to play the Champions League.
"The fans love me and they are one of the reasons why I'm back in Belgrade.''
Boakye's move to China ended in disappointment as he netted just three times in 15 league appearances, involving 13 starts for Suning. He also had to battle with injuries.
''Going to China was a step forward. I consider each step a challenge and lesson. China is behind me, but it remains a lesson,'' Boakye said.
''Not every place can be appealing. It remains regrettable that I did not have the opportunity to work with coach [Fabio] Capello for long.
''Immediately after my arrival, he left the club. He is a great trainer, but I did not have the privilege to learn a lot from him.''