Snapchat CEO, Evan Spiegel, and chief technology officer, Robert Murphy, were in an ownership dispute with Brown following his complaint to the Superior Court of Los Angeles.
Brown reportedly came up with the idea of creating an application for sending disappearing images whilst studying at Stanford University. He then collaborated with Spiegel and Murphy during early development of the app.
The terms of the settlement are confidential.
Spiegel said: “We are pleased that we have been able to resolve this matter. We acknowledge Brown’s contribution and work in getting the application off the ground.”
Snapchat announced the news during the highly-anticipated Apple iPhone launch on 9 September.