Both are due to join the Rangers squad at their training camp in Tenerife, which begins today.
He had an impressive four seasons, which saw Jermain Defoe voted Tottenham's Player of the Year in 2004, netted 50 goals for the club in all competitions and compete in the UEFA Cup for the first time.
McCrorie has made 19 appearances this term and has only recently made a consistent run of starts.
Getting the opportunity to work with Steven Gerrard, someone he has played against on many occasions before the Rangers boss hung up his boots, is something that excites the experienced Davis.
"I'm delighted to be able to welcome Jermain to Rangers", Gerrard told the Rangerswebsite.
The striker, who played for the south coast club in the 2000-2001 season when they were in League One (then the Second Division), has struggled to make an impact in his second spell since joining the club on a free transfer in the 2017 summer window.
The last couple of years have been more challenging, but I believe the management and quality within the dressing room can bring success back.
With Kilmarnock winger Jordan Jones and Dundee midfielder Glen Kamara having signed pre-contracts to move to Ibrox in the summer - and the possibility of those moves being accelerated this month - Rangers have moved quickly to tie down targets.