Reports suggest that the former De Graafschap boss could be installed as early as today.
A Melbourne Heart insider said: "We thought he was the best equipped of the eight candidates. There's a big Dutch presence at the top end of Australian football already and we like the direction that has taken.
"He can't start recruiting officially until October, but it's obvious that the sooner he gets here the better because there's a lot to be done before we enter the competition next season.
"We've given this a lot of thought. We haven't rushed into it and were convinced it will turn out to be a wise choice. We thought recruiting a well-credentialled foreign coach would be our best option."
It is believed that van Stee will sign a two-year deal.