The two guards received all 100 first-place votes from a panel of sports writers and broadcasters. Both players helped their teams reach the second round of the playoffs.
Boston's Jayson Tatum also was selected Tuesday to the first team, falling one vote short of unanimous. Simmons, Mitchell and Tatum are the three finalists for the NBA's Rookie of the Year award.
Celtics coach Brad Stevens said Tuesday that "somebody made a mistake" when asked how Tatum missed out on being a unanimous selection by one vote.
The NBA noted the individual balloting of voters won't be revealed until after its award show following the season.
"He's had an unbelievable rookie year," Stevens said of Tatum. "I know that any awards that come his way is well-deserving."
Information from The Associated Press and ESPN's Chris Forsberg was used in this report.