The former FBI director was speaking at Tabor Academy, a small boarding school in Marion, Massachusetts, on the shores located near Cape Cod. His speech on Monday was his first public appearance since being named special counsel.
Mueller's granddaughter was one of the 133 graduates and she delivered the introduction for Mueller, describing him as a positive role model who cherished his public service.
Mueller did not mention the Russia investigation, but the schoolmaster joked before his address that Mueller has "a few things going on" right now and thanked him for making time for the speech.
He urged students to value integrity.
"When given the opportunity to address students, I always mention integrity because it is so essential to who and what you ultimately will become," Mueller said. "Whatever we do, we must act with honesty and with integrity, and regardless of you chosen career, you are only as good as your word."
Mueller also said "nothing else matters" if you aren't honest.
"You can be smart, aggressive, articulate and indeed persuasive, but if you are not honest, your reputation will suffer, and once lost a good reputation can never, ever be regained," Mueller said. "As the saying goes, if you have integrity, nothing else matters, and if you do not have integrity, nothing else matters."
Later in his address, Mueller said that patience was also an important part of life, and that it is "an acquired skill" that he is still working on. That skill will be crucial as he takes on the widening investigation into Russian meddling in the 2016 election, which could drag out for years.
Tabor Academy announced Muller as its graduation speaker on April 27, three weeks before Deputy Attorney General Rod Rosenstein appointed him to serve as a special counsel overseeing the Russia investigation.
Back in Washington, the investigation continues into Russian meddling in the 2016 election.
The federal probe is widening, and investigators are now looking at senior White House adviser Jared Kushner. There are no indications that Kushner is a target of the investigation, but the FBI is focusing on his involvement in the Trump campaign's data operation, Kushner's own contacts with prominent Russian government officials and his relationship with former national security adviser Michael Flynn.
Former FBI Director James Comey, who was fired by President Donald Trump, will testify soon before Congress. But he wants to talk with Mueller before going public, House oversight committee chairman Jason Chaffetz told CNN last week
. Chaffetz has invited Comey to testify at his committee.
Mueller is no stranger to the Bay State, where he'll be spending his Memorial Day this year.
Before joining the FBI, Mueller worked as an assistant US attorney in Boston. He worked under Bill Weld, the US attorney for Massachusetts who later served as the state's Republican governor in the 1990s. Last year, Weld was Libertarian candidate Gary Johnson's vice presidential running mate.
In addition to his widely respected government service, Mueller previously worked for private law firms in the Boston area, including Hale and Dorr and Hill and Barlow, according to Boston Magazine.
He most recently worked for WilmerHale, and he resigned that position upon becoming special counsel. Two of his colleagues form that law firm joined him to work on the Russia investigation.