Netherlands international De Jong has faced criticism from some sections since joining Barca from Ajax in a reported €75million transfer last year.
De Boer believes his compatriot has adapted well to life at Camp Nou, however, with former team-mate Matthijs de Ligt's early struggles at Juventus being held up in comparison.
"People said he didn't reach the level he reached with Ajax last season in Europe or with the national team," De Boer told BarcaBlog.
"But not everyone can say that they play so many minutes with such a strong team, so I think he's doing well.
"You see how another young player like De Ligt had a harder time, while everyone thought he would play regularly from the start.
"He is doing very well when you consider that this is his first season."
De Jong has two goals in 37 games this term, but De Boer insists it is better comparing him to Busquets, who is regarded as arguably the finest holding midfielder of his generation.
"If he's going to play as a central midfielder, I'm sure he'll be successful," said De Boer, who won the LaLiga title with Barcelona in 1998-99 before joining Rangers the following year..
"He is a controller, you should not ask him to score 20 goals, he is not such a player.
"I am sure he will be a great successor to Busquets in the future."