Mazzulla, 37, who coached the Celtics to a record 18th NBA championship 2024, is the first Boston coach to earn the accolade since Bill Fitch in 1980.
The Celtics, who were eliminated by Philadelphia in the opening round of the playoffs, entered this season without injured star Jayson Tatum.
But they finished with a 56-26 record to take second place in the Eastern Conference standings.
Mazzulla dedicated the honor to the Celtics' entire backroom staff.
"Thank you to our players who compete and give it everything they have each night," Mazzulla said in a statement.
"I am grateful for every member of the Celtics organization whose dedication impacts winning every day.
"This award belongs to our staff, who are there for the guys every day. Their relentless work ethic improves our team daily. This award should be named Staff of the Year."
Celtics president of basketball operations Brad Stevens paid tribute to Mazzulla's team-building in the absence of Tatum, who only returned to the team in March following an Achilles injury last year.
"With all of our unknowns entering the season, Joe did a fantastic job building and growing a team," Stevens said.
"He pours everything he has into competing at a high level ... Joe leads with an authentic care for the Celtics and everyone he works with - players, coaches, and staff."