Koeman took charge at Everton after moving from Southampton earlier this month.
The Dutchman was confirmed as the new Everton manager earlier this month after Roberto Martinez was sacked at the end of last season.
The Blues are hoping he can turn around their fortunes after two disappointing 11th-placed finishes under Martinez in the last two seasons.
They are confident he can do so too, given the success he enjoyed at Southampton during his two years in charge at St Mary’s, which culminated in the qualification for European football last season.
Another who is confident is Koeman's former associate Beenhakker, who not only worked with him during his playing days but also appointed him as manager at Ajax in 2001.
“I don’t know exactly the squad of players at Everton but, as I said before and at the beginning, he is a great manager,” he told evertonfc.com.
“In that way, he is perfectly able to manage the technical part and the people. I’m sure he will be very successful.”
It now remains to be seen if Koeman can be a success at Goodison Park, with the work he does in this summer transfer window likely to be a crucial factor.
It is believed that the Dutchman has been strongly backed by majority shareholder Farhad Moshiri, with a busy summer anticipated as a result.
Should he manage to enjoy success in that regard and bring in the required players then next season could prove to be an exciting one for Everton fans.