Lara was Hyderabad's batting coach and strategic advisor for the 2022 season, during which they finished eighth out of the 10 teams after losing eight games.
"The cricketing legend Brian Lara will be our head coach for the upcoming #IPL seasons," Sunrisers tweeted.
Moody leaves the team after his second stint as head coach following a spell as their director of cricket.
The former all-rounder was recently named director of cricket for the Desert Vipers in the United Arab Emirates' International League Twenty20 competition.