The two 21-year-olds went head to head for the race win in Spielberg last Sunday, with Verstappen coming out on top after pulling off an overtake in the last handful of laps.
Brawn states that despite Leclerc's defeat, he is still getting "better and better" at Ferrari and has shown added maturity in recent races.
"I’m particularly pleased that the top two finishers make up the youngest pairing ever to come first and second in a Grand Prix," Brawn wrote in his post-race column.
"Max Verstappen and Charles Leclerc both deserved to win and if they had finished in reverse order it would have been equally laudable.
"Max drove an amazing race, particularly when one considers that his start, to use a word that’s popular in this sport was ‘sub-optimal’.
"He produced some superbly aggressive passing moves, drove some very fast laps on tyres that had done more than 30 laps, and his race pace management was pretty much perfect.
"Charles also put in a superb performance – dominating the opening sessions and delivering great pole laps. However, for the second time this year he saw his chances of winning evaporate almost within sight of the flag.
"These two kids are definitely promising a brilliant future for Formula 1 in the coming decade."
Ferrari confirmed after the race that it wouldn't appeal Verstappen's overtake on Leclerc, as the pair banged wheels which forced Leclerc to go off track.
Brawn is pleased with the decision, and also believes that there are encouraging signs emerging from Ferrari, despite the continuing run of zero wins in 2019.
"It turned out to be another disappointing weekend for Ferrari, after the team had shown it was a more than a match for Mercedes.
"But there were some encouraging signs for Mattia Binotto and his crew and hats off to them for thinking of the greater good of the sport by saying that the team would not appeal the Stewards’ decision.
"The car is certainly more competitive now than in Barcelona, Leclerc is getting better all the time and Vettel produced a determined drive after a reliability problem in qualifying meant he had little chance of winning the race.
"There’s still some work to do, but the team is on the right road and I’m sure the Scuderia will be rewarded soon."