First, be careful if you keep US citizenship, RESP / TFSA's are not recognized yet as tax deferred pension/ saving accounts by the usa and they will make you pay if you are a US citizen because you still need to file us tax returns. RRSPs are recognized, so are viable, but can also have US income tax questions.
To your question -- you can keep your US accounts, if you have an account with a brokerage that allows Canadian residents. Call and ask, and / or find one that will let you.
If you need to set up a new account with a new bank, you can roll over your investments, so do it. Much better than having your accounts instantly frozen when you leave (or worse, instantly sold and converted to cash). Also, convert your 401k to traditional IRA before you go. IRAs have much more clear language in the tax treaty (as recognized pension funds), and have clearer rules about transfer to Canadian pension accounts.
Because...
You CAN roll over the IRA to a canadian RRSP after you are here, if you don't want to keep it locked in the USA. Your us bank may withhold the 10% penalty and 15% withholding tax (be certain you fill out the form to keep it to 15% per canadian tax treaty) when you with draw, but you can get this full amount back.. Here is how...
It is considered income when you withdraw from the US accounts, even if you roll it over to an RRSP.
Top up the amounts withheld by the USA bank and put the full amount into your Canadian RRSP as a IRA / RRSP rollover.
You will pay taxes on the withdrawal in your canadian taxes... (so pay tax twice, once to canada, once to usa)
And get an offsetting deduction for the RRSP contribution. (Canadian net tax is zero)
Then, you can also claim the amount withheld by the US (15% plus 10% penalty) as foreign taxes on your Canadian return, ... IF you have more than enough Canadian taxes to absorb the deduction. You don't get any extra back. AND you can only do this a single time, not over several years, so you need a very large CDN income year.
The catches
1) you need a large CDN income to claim all the foreign tax credits fully in one year. Talk to a CPA to run the numbers before you do this. The calculation is a bit tricky.
2) CRA will limit the amount that can be rolled over to a mystery number not published anywhere, around $250k, but I can't find where it is written... excess of this mystery number will reduce your RRSP available contribution room. So be careful if you don't have a lot of RRSP room and are moving more than $250k.
3) Canada did not use to allow the 10% penalty to be claimed a foreign taxes, but changed the interpretation about 8 years ago... they could change this interpretation again.
The bonus -- it is unclear in the tax code (US) if the penalty needs to be applied to people who have exited the country, so some US banks do NOT charge the 10% penalty, leaving it up to the IRS to ask for it later if they choose to. Other banks charge it automatically and leave it up to you to ask for it back from Canada tax / IRS.