The pair were the subject of bids on the final few days of the transfer window but ‘Gers were able to stave off any advances to keep them at Ibrox.
Croatian striker Jelavic was wanted by Leicester City and also reportedly Liverpool whilst Aston Villa made a late bid for Northern Ireland midfielder Davis but they remain Rangers players and McCoist is extremely pleased as the Glasgow club chases a fourth-straight SPL title.
"I'm delighted that both Nikica and Steven are staying. There was no pressure to sell either player but the club received a serious offer for Nikica from Leicester," he told the club's official website.
"The fact it was rejected sends out a clear message to all Rangers fans and I have no doubt the players we have are more than capable of defending the SPL title.
"It has been a long window with lots of speculation but we have added seven new players while the core of our double-winning side last season has been re-signed.
"So I am more than happy with the squad we have."