Defoe has passed a medical and finalised his switch to Scotland on an 18-month loan from Bournemouth, while Davis has rejoined the Ibrox club from Southampton on an initial six-month loan subject to global clearance.
Davis, a real fans favourite in his first spell here at Ibrox, joins from Premier League Southampton, where he has made 226 appearances.
Should the deal progress as planned, Davis is expected to join up with Steven Gerrard's squad at a warm-weather training camp in Tenerife before the domestic Scottish programme resumes later in January.
Davis joined Southampton in 2012 after the left Rangers amid the deep financial troubles which the Glasgow club were facing at the time.
Initially, it was thought that it was Southampton who did not a permanent transfer but that would not make any sense since Steven Davis is out of contract at the club during the summer.
A former worldwide colleague of Defoe, Gerrard is well aware of his talents and enthused: 'I'm delighted to be able to welcome Jermain to Rangers.
In the meantime, the youngster is in desperate need for some game time and may be loaned out away from the Premier League in order to get that.
Defoe has scored goals wherever he has played, 273 of them in a club career taking in the likes of West Ham, Tottenham, Sunderland and Portsmouth.
Hasenhuttl added: "We are open-minded and our eyes are open, so we know in the winter period it is not so easy to find transfers that really help you".