The 43-year-old former Barcelona and Netherlands star is anxious to seek after another challenge after a massive fruitful spell in charge, which began in 2015.
Van Bronckhorst, who began and finished his playing career in Rotterdam, won two KNVB Bekers, two Johan Cruyff Shields and the 2016-17 Eredivisie title, Feyenoord’s first since 1999.
“There is still a lot to fight for this season. We have to secure European football through the league or the cup. I’m looking forward to that,” he told the club’s website.
“At the same time, I’ve been thinking a lot about whether I want to stay for one or more years as head coach of Feyenoord after this season. That was a very difficult decision, because Feyenoord are in my heart.
“However, in my career I have always followed my feelings and my feeling now says I shouldn’t do that.”
Technical director Martin van Geel said: “Gio is really an emotional person. If he has an idea himself of wanting something different after this season, we can only respect that.
“We are already very grateful to him for his great contribution in the recent, unprecedented successful period of the club.
“Whatever Giovanni does after this season, his bond with us and the club will always remain unbreakable.”
And van Geel admitted that his side have not prepared a list of potential replacements yet.
“This gives us the time to find a suitable successor. Undoubtedly, the names of alleged candidates will be flying around from tomorrow, but we are not yet that far. We will take the time to carefully weigh what will be the best for Feyenoord.”