After nine years playing abroad, the former Netherlands international returned to Feyenoord this week after agreeing a one-year deal to move from Fenerbahce in April.
The 34-year-old joins a side that finished fourth in the Eredivisie last term while making the round of 32 in the UEFA Europa League.
Feyenoord are without a title since the KNVB-Beker in 2008 and Kuyt told a news conference: “One of the disappointing things from my first spell is that I never won a trophy. I certainly have the ambition to do that this time.
“Feyenoord’s financially difficult period is behind it and a very talented team has been put together. Last season, they showed that there’s a lot of quality here, not least against Roma, Sevilla and PSV.
“It’s just that the end of the season did not go as planned. This season the focus is on reproducing the performances in those good matches and keeping it going longer than last year.
“What’s most important is leading the way on the field, as I tried to do in my first period. I’ve returned to Feyenoord full of ambition and I feel as strong as I ever have in the past.
“People were very appreciative and respectful when it was first announced that I would join Feyenoord. To also experience a first day of training like this, with so many people showing an interest, has an effect on you.”