Van Gaal signed a three-year deal at Old Trafford earlier this week to replace David Moyes, who was sacked last month after a horror season in which United finished seventh in the Premier League and failed to qualify for Europe.
Van Gaal, who describes himself as "confident, arrogant, dominant, honest, hard-working and innovative" arrives with a proven track record having won league titles at Ajax Amsterdam, Barcelona, AZ Alkmaar and Bayern Munich as well as the Champions League in 1995.
His approach has been described as "strict" by former Netherlands midfielder Ronald de Boer but Van Persie said he favours his compatriots managerial style.
"It is a different sort of approach to what I was used to with previous coaches but I like it," Van Persie told The Sun on Sunday.
"It is a very Dutch way of doing things - very direct but intended to make us better players."
Van Persie arrived at Old Trafford in 2012 and fired United to the title with 30 goals in all competitions but endured a frustrating campaign last season that was disrupted by injuries.
The 30-year-old has a strong relationship with Van Gaal having been named the permanent captain of the Netherlands national team last year.
Van Persie had been linked with an exit from Old Trafford but following the arrival of Van Gaal has given the strongest indication yet that he may remain at United.
"I have enjoyed the past two years with Holland a great deal," he said.
"He is very clear in what he says. I am now going to go through another two-year process with Van Gaal and I am looking forward to it."
Van Persie's United team mate, Danny Welbeck, echoed his sentiments regarding the 62-year-old's appointment.
"I am happy. He is a great man, a great manager. Looking at his CV tells you he has managed at some big clubs," he said.