Livingstone was the first player picked by Melbourne Renegades in August and was the most sought-after player in the draft as the BBL looked to reinvigorate the tournament ahead of the next Cricket Australia TV rights negotiation which is set to be finalised in 2024.
"We're obviously disappointed that we won't have Liam as part of our team this summer, but we understand his decision," Renegades general manager James Rosengarten said.
"Liam is a fantastic cricketer and there's a reason we used our first pick in the draft to select him. Since then, his schedule has changed with added international duties and we wish him the best as he pushes for a Test debut.
"We know Liam had been looking forward to working with our head coach, David Saker, and playing for our club. Hopefully, we can make that happen in the coming seasons.
"We have been in regular communication with Liam and his management over the last couple of months, which has allowed us to execute a plan that is best for the Renegades for this season.
"We've already secured Andre Russell for the first four matches and know the match-winning ability he will add to our team.
"This news has allowed us to explore replacement options with greater availability beyond the first half of the tournament, and we look forward to being able to announce another big-name addition for the Renegades soon."