Healy arrived at Ibrox on Sunday fresh from a disappointing spell at Sunderland, who had loaned him out to Ipswich and Doncaster.
The striker will be looking to get off to a better start with Rangers as he prepares to make his debut in Sunday's Scottish Cup fifth-round tie against Celtic at Ibrox.
Healy has been something of an enigma throughout his career with an exceptional goalscoring record at international level never matched by his domestic form.
Although he has enjoyed productive spells at Preston and Leeds, he also failed to secure a regular spot at Fulham, where he played alongside Davis.
But the 31-year-old has scored a record 35 goals for Northern Ireland and was the top goalscorer in the Euro 2008 qualifiers, helped by a hat-trick against Spain, the eventual winners and current world champions.
Davis told Blues News: "There is no better finisher out there. I've played with him for a number of years with Northern Ireland and for six months at Fulham as well. He's a really, really good finisher.
"If we create chances he will be sniffing around the box and put them away. He is a good player and a good person to have around the dressing room."