Sir Kenneth Calman, who was before the House of Lords Constitution Committee, also said he believed such a document could define what it was to be British.
He told members that not enough had been done to "articulate" the case for the Union.
In 2009, the Calman Commission recommended that Scotland take charge of half the income tax it raised.
His report, which included input from the three main Unionist parties but not the SNP, came five years before the Scottish independence referendum in September 2014.
I don't think [the case for the Union] has been well enough articulated - it is still a case of 'them at Westminster'
Sir Kenneth appeared before the committee - which has no SNP members - alongside Sir Paul Silk, former chairman of the Commission on Devolution in Wales.
Crossbench peer, Lord Judge, asked if there was merit in creating a Charter of the Union.
Sir Kenneth replied: "The answer is yes. I think it would make the discussion easier about who does what, and how we benefit, how you benefit and how we all benefit. I think that would be very helpful.
"Without that communication, the average citizen is left wondering who does what for me now - and it is Westminster's fault anyway - so, it is easier to put it the wrong way."
Sir Kenneth was also asked, by Labour peer Lord Morgan, whether such a charter should include suggestions on what it was to be British.
The former chief medical officer of Scotland said: "I think that is a good point, that seems to be part of the [means to an] end, what does it mean to be a citizen of this country and what are our values.
"I can see that a group could look at a range of these issues, articulating, communicating them and seeing if people want to be part of it."
The former commission chief added: "I don't think [the case for the Union] has been well enough articulated - it is still a case of 'them at Westminster', as opposed to 'Westminster is here to help you'.
"We need to show that it [the Union] is worthwhile, not only that Scotland has something worthwhile to contribute to the UK parliament and the UK in general, but that is what the UK is for."
The man who led a review of Scottish devolution has given his backing to a so-called "Charter of the Union".