The former Atletico Madrid and Everton defender was moved from Jong Ajax, the club’s reserve team who play in the Dutch second division, to take over the first team last weekend as caretaker coach after Alfred Schreuder (50) was sacked.
Ajax beat Excelsior Rotterdam 4-1 away in his first game in charge on Sunday.
The club said Heitinga would stay in charge for the rest of the season, with the experienced Dwight Lodeweges appointed as his assistant.
"We are convinced that this is the right solution. John has followed a careful and gradual path, which has allowed him to develop very well as a coach in recent years," said a statement from general manager Edwin van der Sar.
The win allowed Ajax to move up one place in the Dutch standings to fourth, five points behind leaders Feyenoord. Defending champions Ajax are away at Cambuur Leeuwarden on Sunday.
The 65-year-old Lodeweges was assistant and interim coach at PSV Eindhoven and the Dutch national team.
Schreuder was sacked after a series of poor results just six months after taking over from Erik ten Haag, who moved to Manchester United.
