"When we saw the man wielding a knife, instinct took over and we were able to... successfully detain the male," Valentine said.
Chief Constable Paul Crowther said, "I think they were heroes - they don't think that themselves. They were really concerned for the other people who were injured and for the Metrolink staff."
He added: "Their quick-thinking and outstanding response helped to prevent more passengers being hurt and stands as a testament to the force."
Sergeant Valentine was wounded in the incident, suffering several lacerations. He was transported to a nearby hospital where he was treated and released.
No details have been released on the status of the victims of the knife assault.