The 30-year-old NBA star had been serving a suspension imposed by the Nets on November 3 for sharing a social media post on a book and film that featured anti-semitic tropes.
Irving verbally apologised for the post for the first time on Saturday, saying he was "deeply" sorry to the Jewish community.
The Nets initially listed Irving as "questionable" for the Grizzlies clash at Barclays Center, before confirming on Sunday he would be available.
Irving said he has been on a "learning journey" as part of his suspension and reintegration into the Nets team, before reiterating his sorrow to reporters on Sunday, offering: "my deep apologies to all those who are impacted over the last few weeks".
"I don't stand for anything close to hate speech, or anti-semitism, or anything that is anti going against the human race," he said. "I feel like we all should have an opportunity to speak for ourselves when things are assumed about us.
"And I feel it was necessary for me to stand in this place and take accountability for my actions because there was a way I should have handled all of this.
"... I meant no harm to any person, any group of people. And yeah, this is a big moment for me because I'm able to learn throughout this process that the power of my voice is very strong.
"The influence that I have within my community is very strong, and I want to be responsible for that. In order to do that, we have to admit when you were wrong and instances where you hurt people and it impacts them."
Irving has played just eight games this season as a result of the ban, averaging 26.9 points, as well as 5.1 assists and 5.1 rebounds.