The Englishman joined the Dons during the summer after being released by Coventry City.
He has had an impressive start to his career in Scotland and has become a very popular player with the Red Army.
He told RedWeb: "I like the lads. They are a great bunch of lads, I like Archie, I like the gaffer. Everyone around the club is very friendly. There is a very promising future at this club. I want to be part of it.
"Also the Aberdeen fans have been absolutely brilliant towards me. They have embraced me. At the start of the season they would all sing my name and at the time I was not playing that well, so it gave me a lot of confidence. Their support means a lot to me.
"I did not bother speaking with my agent to see what offers there were down south. I just wanted to stay here.
"I could not turn down the offer to stay on at such a big club. Hopefully if not this season, next season we will get into a cup final or into Europe. I want to be part of that.
"At a club like Aberdeen there is more opportunity to win something than playing for a team down south. There is a lot to look forward to.
On his current injury problems, he added: "My hamstring is getting there, I have doing a lot of work with John Sharp and David Wylie. Hopefully I will be back soon though and can help the team during the final months of the season."
Boss Craig Brown was delighted that Osbourne put pen to paper. "I spoke to him yesterday and he had a big smile on his face," said Brown. "He is happy to be here.
"The players seem to enjoy it and the response of the fans to Osbourne and all the new players has been exceptional."