Farke, 48, led his side to a memorable Championship title with a 2-1 win over Plymouth on Saturday.
Despite earning promotion back to the Premier League, multiple reports had suggested the German may still be sacked over doubts regarding his ability to manage in the English top-flight.
Speaking to BBC Radio Leeds, Marathe has rubbished the chances of Farke leaving the club, backing his manager.
Marathe said: "I have ended the speculation. He is my man. I want to tell you all I'm very excited to run it back with Daniel.
"I'm really excited about collaborating with Daniel, with (managing director) Robbie Evans, with (sporting director) Adam Underwood and, together, we are going to build the best squad we can with every penny we're allowed to spend to compete in the Premier League."