Martino, affectionately known as 'Tata', was announced as the successor to Tito Vilanova on Tuesday.
The Argentinian had never managed in European football before his appointment, but the decision has proved a popular one with Barcelona's players, with Lionel Messi and Andres Iniesta both praising the move.
Cruyff, now an advisor at Ajax, was in charge at the Camp Nou between 1988 and 1996.
The 66-year-old admitted he has little knowledge of Martino, but does not feel that will have an impact on Barcelona's dominance of the Spanish game, citing the examples of Frank Rijkaard and Pep Guardiola as precedents.
"I don't know Tata very well," Cruyff told Voetbal International.
"I have no doubt that Barcelona can continue the same way.
"Rijkaard and Guardiola had won nothing when they started at Barcelona, and yet they ended up being hugely successful."
