It was announced on Monday that Fletcher, 36, has made the step up from working with the club's under-16s academy side to coach United's first team.
He replaces Solskjaer's longstanding assistant Mark Dempsey, who has gone the other way into a role with the academy.
"He's got the Man Utd DNA and there was a spot open because Mark Dempsey has moved to the academy," Solskjaer said. "We felt he was so valuable there, he's been brilliant in the academy and helping out.
"Then when this opening came, Darren has been away from the club a few years but then he's come back doing coaching with the 16s and with his experience of being here through both successful and difficult times, we felt it was right now for Darren to come in and give us that input."
He also said, "I think it's also important that we bring ex-players that have been somewhere else.
"I've been somewhere else after having worked under Mick Phelan, Sir Alex [Ferguson] and Carlos [Queiroz]. We know one way of the coaching but they've been at different clubs and got different ideas.
"Fletch, with his ideas and thoughts, will improve us in the backroom staff."
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