The 26-year-old right-footed centre-back spent two years at Tannadice and moves to Pittodrie after his contract ran out at the end of May.
Morris, who has represented Republic of Ireland at U21 level, told RedWeb: "I am very excited to be here and looking forward to getting started.
"I was pleased to get everything finalised so I could get myself ready for pre-season and I can come in and meet the boys straight away.
"I got a call from my agent to say the manager had been in touch. As soon as I heard that I had my mind set on coming up here. It is obviously a huge club with a very good squad and they showed that when they pushed Celtic all the way last season.
"What an opportunity it is for me. It is something any player would jump at the chance to be part of. I am really looking forward to the European games starting later this month."