Cummins won the men's award after a year in which he led Australia to the World Test Championship and World Cup titles.
"It's a huge honour. It has been a big year, lots of wonderful team success," Cummins said.
"To get this individual honour is huge and I am pretty amazed. In terms of individual accolades, it is right up there."
England all-rounder Sciver-Brunt won her second successive Women's Cricketer of the Year award, after consistent performances in all three formats, scoring 137 runs in two Tests, 393 runs in six ODIs and 364 runs in 10 T20Is.
"It feels pretty special," Sciver-Brunt said.
"I wasn't expecting it as I was coming up against some players that have done so well in 2023. I’m really pleased and pretty proud."
Australian opener Usman Khawaja was named the ICC Men's Test Cricketer of the Year, while Virat Kohli won his fourth ICC Men's ODI Cricketer of the Year award after guiding India to the Cricket World Cup final.
Sri Lanka's Chamari Athapaththu won her first ICC Women's ODI Cricketer of the Year, taking the award ahead of Sciver-Brunt.
England's Richard Illingworth won the Umpire of the Year for the third time, and Zimbabwe Cricket won the ICC Spirit of Cricket Award for their sporting conduct after their win over West Indies in the World Cup qualifier match in June.
