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Morris has spent three seasons with the Linnets, and will now link up with FC United following their relegation from National League North.
Manager Michael Ellison said: "We are obviously sorry and disappointed to see Aaron go as he has been a top player for us.
"We tried our best to persuade him to stay but he was keen to prove himself at a higher level and I am sure he will do well for FC United on their return to the EVO-STIK League Premier Division.
"We now begin the search for a replacement for Aaron while thanking him for his service to Runcorn Linnets and wishing him well at his new club."
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