The veteran Spaniard ended his playing career to take on a backroom role with the Catalan club this summer, leaving his shirt number vacant after he first took it over from Abelardo in 2002.
The 36-year-old, who captained the club to three Champions League titles amongst numerous other trophies, personally requested that Busquets inherited his squad number.
Busquets, who came through the ranks at Camp Nou and has worn No.16 for almost all of his first-team career with the club, voiced his pride at following in the footstepts of Puyol.
"It's an honour to be able to wear the No.5 jersey and that Carles Puyol thought of me to inherit it," he told the club's official site.
Puyol himself later tweeted his confidence that Busquets was the right man to take on the number.
"I've not doubt the No.5 shirt is in the best hands," he said. "I'm sure he will look after it."