The 31-year-old forward has yet to feature for the Millers this campaign and is looking forward to playing regular first-team football during his spell with the Sky Bet League Two outfit.
Odejayi told the club's official website: "This move could have happened sooner but for whatever reason it didn't.
"I'm here now, raring to go and looking forward to getting started.
"I want to come here, get some games and hopefully score some goals and help the club to improve our league position and get as high up the table as possible."
Stanley boss James Beattie is thrilled to have finally signed the former Barnsley marksman, who he has had his eye on for some time.
"We're delighted to have Kayode in," Beattie said. "This is something I've been working on for two or three months and we were unfortunate not to get him permanently.
"He's trained with us this morning (Tuesday) and he's exactly what we need, what we have been missing and hopefully he'll be the missing link to get us going."