The former Brentford man joined last month and has been quick to make his mark at Ibrox.
“I know just how exacting it is and Davie will know it from his days as a player,” said McLeish.
“I think it will definitely be beneficial to Mark to have Davie there. If Mark had brought someone else in, there may have been more questions about him from people, but having Davie there softens that.”
McLeish spent four and a half years as Rangers manager between 2001 and 2006 - enjoying two league titles, two Scottish Cups and three League Cups – and is well versed on the highs and lows of life in the Old Firm.
The Aberdeen legend feels a good start is crucial if Warburton is to avoid the build-up of pressure that can quickly develop at Ibrox.
“If Mark gets off to a good start, he will find that it turns from being absolutely vice-like to something you are happier dealing with.”
“When it is not going so well at a club such as Rangers, though, it can really drain the life out of you. There is no doubt about it. I was certainly a little bit drained at the end of my time as manager.”
Warburton will no doubt face his ups and downs as Rangers gaffer, but his start to life at Ibrox has been a confident one and in David Weir he has an experienced and wizened aide to help him through the stickier patches.