Here, the PA news agency looks at the in-tray awaiting the former Gers player.
Fixing cup drought
The first of several things that the Dutchman will have to deal with is the Premier Sports Cup semi-final against Hibernian at Hampden Park on Sunday.
The Light Blues have not won a major cup since the League Cup final win over Celtic in March 2011 and it is the one thing that was held against Gerrard before he left for the midlands last week.
van Bronckhorst’s return to Glasgow is subject to receipt of a work permit and he will not be in the dugout on Sunday, although he will be in the stadium.
However, it would be the perfect start if Rangers could book a place in the December final against either Celtic or St Johnstone.
Maintaining lead in cinch Premiership
Gerrard brought the Premiership title back to Ibrox for the first time in a decade last season and in doing so stopped Celtic winning their coveted 10-in-a-row.
After 13 league games, the former Liverpool and England captain left the Ibrox club in a good position, four points clear of their Old Firm rivals at the top of the table.
After the excitement of his appointment has died down, the pressure will be on van Bronckhorst to maintain those league placings all the way until the end of the season to clinch title number 56, and perhaps add a domestic cup or two.
Rangers still have Europa League ambitions as the tournament gets set to return next week and van Bronckhorst does not have much time to prepare for that either.
The Govan club are sitting in third place in Group A, eight points behind runaway leaders Lyon and behind Sparta Prague only by dint of their 1-0 defeat away to the Czech outfit.
However, Rangers host Sparta Prague at Ibrox on Thursday before an away game against Lyon to finish the section.
It is in the Gers’ own hands to get through to the last-16 for the third successive time and achieving that would give van Bronckhorst some early kudos.
Identifying playing budget
It is a story as old as the Bosman rule. Centre-back Connor Goldson’s contract is due to run out in the summer and he has yet to sign a new one.
This, of course, allows the former Brighton defender to speak to clubs in January.
In addition, the Govan club’s accounts for last season showed a £23.5million operating loss so what assurances has the new Rangers boss been given with regards playing budgets and the buying and selling of players and how will that impact his squad in January and next summer?