Strachan took charge of Scotland in January and has won two of his five World Cup qualifying matches since then, including an impressive away victory over Croatia in June.
The veteran manager has also lost to Wales, Serbia and Belgium since taking over, as well as a friendly defeat to England, but Stimac believes that Strachan is the man to lead Scotland to a first major tournament since the 1998 World Cup.
"Definitely. You can expect him good things with Gordon as the manager. He is a key man for your success. You can already see that he is constructing the team for the next qualifiers. Before him, you didn't look well to be honest," Stimac is quoted as saying by PA.
"I wasn't happy that the last manager was going and Gordon came in. I knew that changes would be made and your team would perform in a different way and he is putting things in the right place. I am quite sure that Scotland will be tough opponents in the next qualifiers.
"Gordon is a great guy, a great character. I know him from his Coventry days, the 1995/96 season. He always had his big smile at grounds where I went to watch European Championships and World Cup games and it was always nice to speak to him. Looking at the Scottish team now, I would say that you are on the right track."
Croatia face Scotland in their final World Cup qualifying match tomorrow, although their hopes of finishing top of Group A were dashed by a 2-1 defeat to Belgium on Friday.