The 32-year-old was released by the Robins at the end of the season and opted to move to the A-League rather than accepting a one-year contract at Brighton.
Owusu told Adelaide's official website: "I got a feel of the city while I was in Adelaide and I was made really welcome by the club and the players were top draw. I felt like I had already been there for a season, all the coaching staff were brilliant.
"I will be coming to Adelaide wanting to score goals and hopefully get the club up where they want to be and picking up trophies, so if I can add a bit of quality to the team of what they already got it's going to be good for everyone."
Adelaide coach Aurelio Vidmar added: "He's got a fair bit of experience and knows how to score goals. We're looking for a big input from him."