The 30-year-old stumped Pakistani batsman Umar Gul for 12 on the third day of the first Test against Pakistan at the National Stadium in Karachi to reach the milestone.
"It's a great feeling to have broken the record, especially of someone who I used to watch on television as a schoolboy," Boucher said at the end of the day's play.
Boucher, who made his Test debut against Pakistan at Sheikhupura in 1997, has 378 catches and 18 stumpings from 103 Tests. He is regarded as one of the world's best keepers and is also a dependable batsman.
Healy, who retired in 1999, had 366 catches and 29 stumpings in 119 Tests.
Boucher said Healy was a great wicket-keeper.
"Healy was great and I used to love the way he kept (wicket). In a way it's a great feeling but it is also sad to break such a good keeper's record," he said.
"I have played enough Tests so if you play over 100 Tests, records come your way.
"But this is the best record I have achieved and I am happy with that."
Boucher added that it would "be the cherry on the top if we win the Test."
The tourists finished the third day at 76-3, having an overall lead of 235. Left-arm spinner Paul Harris took 5-73 to help South Africa dismiss Pakistan for 291 in the first innings.
The visitors made 450 in their first innings on the back of a masterly 155 from Jacques Kallis.