We're now ready for our next chapter.
Systrom issued a statement on Instagram's blog, saying that he and Krieger were "planning on taking some time off to explore our curiosity and creativity again".
Facebook boss Mark Zuckerberg said: "Kevin and Mike are extraordinary product leaders and Instagram reflects their combined creative talents". I've learned a lot working with them for the past six years and have really enjoyed it.
Zuckerberg also said he was looking forward to seeing what Systrom and Krieger build next.
When Facebook bought it up, Instagram was ad-free and had a following of 31m people.
It's the latest in a wave of executive departures of recent times, one that's proven a particular headache for Facebook.
The pair will depart soon, according to the company.
Systrom and Krieger notified the photo-sharing app's leadership team and Facebook on Monday about their decision to leave, Instagram said.
The cofounders of Facebook's photo-sharing app Instagram have resigned their positions and plan to leave the company in coming weeks, the New York Times reported Monday evening.
Facebook acquired Instagram for $1 billion in 2012, and since then, it has been considered one of the social media network's most successful acquisitions. In 2016, it added the ability to post slideshows that disappear in 24 hours, a copy of Snapchat's popular "stories" feature.
The photo app's global revenue this year is likely to exceed $8 billion, showed data from advertising consults EMarketer. A new privacy law in Europe has also affected prices.