The German, who last September became the first foreigner to coach Bulgaria since 1966, had signed a one-year contract with an option for two more years but led the team to only three wins - two of them in friendlies - in 11 games.
Bulgarian Football Union President Borislav Mihaylov criticised Matthaus for living outside the country for most of the time, adding that it had influenced results and preparation of the team. The BFU said his contract would not be renewed and under-21 coach Mihail Madanski stepped in on a temporary basis.
Bojinov, who clashed with Matthaus and was omitted from the national squad several times in the last year, told Meridian Match daily on Monday he was pleased the new coach was Bulgarian and could communicate with players.
"It was a different story with Matthaus, it was like a broken phone conversation," said the Sporting Lisbon forward, who has 33 caps.
"You're talking to a translator and you know that sometimes such 'tactics' leads to problems. One didn't hear something, others didn't understand something... much of it was lost in translation."
Matthaus captained West Germany to their 1990 World Cup win and has a record 150 caps but he has achieved limited success as a coach with Rapid Vienna, Partizan Belgrade, Atletico Paranense, Salzburg, Maccabi Netanya and Hungary.
