Robson becomes Dons manager Derek McInnes' second signing of the close -season, with Dundee United midfielder Willo Flood having already joined on a similar pre-contract agreement.
The 34-year-old has represented Inverness, Dundee United, Celtic, Middlesbrough and Vancouver Whitecaps during his career and has also earned 17 caps for Scotland.
"Barry is a player I know well and having been a team-mate of his I can see the same hunger and determination within him as he had when I played alongside him," McInnes told Aberdeen's official website.
"It's clear to see he has retained a high level of performance.
"Both Tony (Docherty) and I have watched him recently and have only had good reports about his performances for Sheffield United.
"We still feel he has that winning mentality and is someone who can bring some real quality to the team. We're delighted to have him on board and as a local boy I'm sure he is looking forward to playing for his home town team."
And Robson admitted he was delighted to be joining his local club.
"I think it's something I have always wanted to do, it's something my family have always wanted me to do and I am very privileged to be able to join now," he said.
"I know how big a club this is, I know how good a club it is and it's always a club I wanted to play for and I am just glad I am getting the opportunity to do that."