The 25-year-old has proved his fitness to Dons manager Craig Brown, following a lengthy knee injury, after initially joining the club on trial at the end of last season.
Osbourne made the last of his 135 appearances for Coventry in November 2009 but he is confident he can make an impact in the Scottish Premier League.
"The last two years have not been the best for me, obviously I have played very little football, but I can't wait, I can't wait to start as I know this is a top league," Osbourne told RedTV.
"I had a lot of doubts in my head, I thought I might not even play again.
"To be given another opportunity, I'm going to try and grasp it and do everything to repay the manager, Archie (Knox) and the club for the giving me the opportunity.
"I feel I will be better than ever. Being away for so long has given me more hunger for the game."
Brown, who signed Chris Clark for his second spell at Pittodrie on Wednesday, added: "We have other players in our sights. My phone is red hot and I am speaking to all my contacts down south.
"Our squad is getting more competent but it is not complete as we would like."
Source: Team Talk
Source: Team Talk