The 30-year old Finnish midfielder is back at Rugby Park on a short-term deal following his departure from Kazakhstani outfit Kairat Almaty in November.
Eremenko starred for Killie while on loan from Metalist Kharkiv in 2010/11 and was delighted to be back in Ayrshire, albeit quicker than he anticipated.
"To be honest, I didn't expect to return to the club as soon as I have," he told Sky Sports News.
"I thought I would come back one day, maybe when I was 34 or 35, but that makes no difference. I am just delighted to be back here.
"I'm glad the deal could be done and I can't wait to put the Killie shirt on and get playing again.
"However, my last game was about three months ago so it may take a little bit time before I am ready.
"I'm not match-fit, that's for sure, but I have been training and I just need time...maybe two or three weeks to get my fitness back.
"Hopefully against Dundee United in two and a half weeks I will be ready to return.
"My main mission is to help the team to get to the top six and I hope I don't disappoint the fans.
"I want to help bring the younger players through and if someone needs some advice or help on the pitch then I am happy to help them."
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